Sasi Math (Revised for 1024)

Scroll:Mensuration >> cylinder and rectangular >> ps (4137)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

Water is flowing at the rate of 45 km / hr through a cylindrical pipe of daimeter 42 cm into a rectangular tank which is 150m long and 132 cm wide. In how hours will the water level in the tank raise by 63 cm ( take π = $\frac{22}{7}$ )

132cm

D=42cm

150m

63cm

speed

\frac{45km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 60 km / hr through a cylindrical pipe of daimeter 56 cm into a rectangular tank which is 200m long and 176 cm wide. In how hours will the water level in the tank raise by 84 cm ( take π = $\frac{22}{7}$ )

176cm

D=56cm

200m

84cm

speed

\frac{60km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 105 km / hr through a cylindrical pipe of daimeter 98 cm into a rectangular tank which is 350m long and 308 cm wide. In how hours will the water level in the tank raise by 147 cm ( take π = $\frac{22}{7}$ )

308cm

D=98cm

350m

147cm

speed

\frac{105km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 15 km / hr through a cylindrical pipe of daimeter 14 cm into a rectangular tank which is 50m long and 44 cm wide. In how hours will the water level in the tank raise by 21 cm ( take π = $\frac{22}{7}$ )

44cm

D=14cm

50m

21cm

speed

\frac{15km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 30 km / hr through a cylindrical pipe of daimeter 28 cm into a rectangular tank which is 100m long and 88 cm wide. In how hours will the water level in the tank raise by 42 cm ( take π = $\frac{22}{7}$ )

88cm

D=28cm

100m

42cm

speed

\frac{30km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 120 km / hr through a cylindrical pipe of daimeter 112 cm into a rectangular tank which is 400m long and 352 cm wide. In how hours will the water level in the tank raise by 168 cm ( take π = $\frac{22}{7}$ )

352cm

D=112cm

400m

168cm

speed

\frac{120km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 90 km / hr through a cylindrical pipe of daimeter 84 cm into a rectangular tank which is 300m long and 264 cm wide. In how hours will the water level in the tank raise by 126 cm ( take π = $\frac{22}{7}$ )

264cm

D=84cm

300m

126cm

speed

\frac{90km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 75 km / hr through a cylindrical pipe of daimeter 70 cm into a rectangular tank which is 250m long and 220 cm wide. In how hours will the water level in the tank raise by 105 cm ( take π = $\frac{22}{7}$ )

220cm

D=70cm

250m

105cm

speed

\frac{75km}{hr}

it will take hours to raise the required water level.

Answer:_______________

Water is flowing at the rate of 135 km / hr through a cylindrical pipe of daimeter 126 cm into a rectangular tank which is 450m long and 396 cm wide. In how hours will the water level in the tank raise by 189 cm ( take π = $\frac{22}{7}$ )

396cm

D=126cm

450m

189cm

speed

\frac{135km}{hr}

it will take hours to raise the required water level.

Answer:_______________

10)

396cm

D=126cm

450m

189cm

speed

\frac{135km}{hr}

it will take hours to raise the required water level.

Answer:_______________

132cm

D=42cm

150m

63cm

speed

\frac{45km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 45 km / hr

= 45000m / hr

Diameter of the pipe,

= 2 r = 42 cm

Thus, r = $\frac{21}{100}$ m

Let h be the water level to be raised.

Thus, h = 63cm = $\frac{63}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 45000 m³

= $\frac{22}{7}$ x $\frac{21}{100}$ x $\frac{21}{100}$ x 45000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 150 x 132 x $\frac{63}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{21}{100}$ )² x T x 45000 = 150 x 132 x $\frac{63}{100}$

⇒ $\frac{22}{7}$ x $\frac{21}{100}$ x $\frac{21}{100}$ x T x 45000 = 150 x 132 x $\frac{63}{100}$

⇒ $\frac{436590000}{70000}$ x T = $\frac{1247400}{100}$

⇒ 6237 x T = 12474

⇒ T = 12474/ 6237

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

176cm

D=56cm

200m

84cm

speed

\frac{60km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 60 km / hr

= 60000m / hr

Diameter of the pipe,

= 2 r = 56 cm

Thus, r = $\frac{28}{100}$ m

Let h be the water level to be raised.

Thus, h = 84cm = $\frac{84}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 60000 m³

= $\frac{22}{7}$ x $\frac{28}{100}$ x $\frac{28}{100}$ x 60000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 200 x 176 x $\frac{84}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{28}{100}$ )² x T x 60000 = 200 x 176 x $\frac{84}{100}$

⇒ $\frac{22}{7}$ x $\frac{28}{100}$ x $\frac{28}{100}$ x T x 60000 = 200 x 176 x $\frac{84}{100}$

⇒ $\frac{1034880000}{70000}$ x T = $\frac{2956800}{100}$

⇒ 14784 x T = 29568

⇒ T = 29568/ 14784

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

308cm

D=98cm

350m

147cm

speed

\frac{105km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 105 km / hr

= 105000m / hr

Diameter of the pipe,

= 2 r = 98 cm

Thus, r = $\frac{49}{100}$ m

Let h be the water level to be raised.

Thus, h = 147cm = $\frac{147}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 105000 m³

= $\frac{22}{7}$ x $\frac{49}{100}$ x $\frac{49}{100}$ x 105000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 350 x 308 x $\frac{147}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{49}{100}$ )² x T x 105000 = 350 x 308 x $\frac{147}{100}$

⇒ $\frac{22}{7}$ x $\frac{49}{100}$ x $\frac{49}{100}$ x T x 105000 = 350 x 308 x $\frac{147}{100}$

⇒ $\frac{5546310000}{70000}$ x T = $\frac{15846600}{100}$

⇒ 79233 x T = 158466

⇒ T = 158466/ 79233

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

44cm

D=14cm

50m

21cm

speed

\frac{15km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 15 km / hr

= 15000m / hr

Diameter of the pipe,

= 2 r = 14 cm

Thus, r = $\frac{7}{100}$ m

Let h be the water level to be raised.

Thus, h = 21cm = $\frac{21}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 15000 m³

= $\frac{22}{7}$ x $\frac{7}{100}$ x $\frac{7}{100}$ x 15000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 50 x 44 x $\frac{21}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{7}{100}$ )² x T x 15000 = 50 x 44 x $\frac{21}{100}$

⇒ $\frac{22}{7}$ x $\frac{7}{100}$ x $\frac{7}{100}$ x T x 15000 = 50 x 44 x $\frac{21}{100}$

⇒ $\frac{16170000}{70000}$ x T = $\frac{46200}{100}$

⇒ 231 x T = 462

⇒ T = 462/ 231

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

88cm

D=28cm

100m

42cm

speed

\frac{30km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 30 km / hr

= 30000m / hr

Diameter of the pipe,

= 2 r = 28 cm

Thus, r = $\frac{14}{100}$ m

Let h be the water level to be raised.

Thus, h = 42cm = $\frac{42}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 30000 m³

= $\frac{22}{7}$ x $\frac{14}{100}$ x $\frac{14}{100}$ x 30000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 100 x 88 x $\frac{42}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{14}{100}$ )² x T x 30000 = 100 x 88 x $\frac{42}{100}$

⇒ $\frac{22}{7}$ x $\frac{14}{100}$ x $\frac{14}{100}$ x T x 30000 = 100 x 88 x $\frac{42}{100}$

⇒ $\frac{129360000}{70000}$ x T = $\frac{369600}{100}$

⇒ 1848 x T = 3696

⇒ T = 3696/ 1848

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

352cm

D=112cm

400m

168cm

speed

\frac{120km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 120 km / hr

= 120000m / hr

Diameter of the pipe,

= 2 r = 112 cm

Thus, r = $\frac{56}{100}$ m

Let h be the water level to be raised.

Thus, h = 168cm = $\frac{168}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 120000 m³

= $\frac{22}{7}$ x $\frac{56}{100}$ x $\frac{56}{100}$ x 120000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 400 x 352 x $\frac{168}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{56}{100}$ )² x T x 120000 = 400 x 352 x $\frac{168}{100}$

⇒ $\frac{22}{7}$ x $\frac{56}{100}$ x $\frac{56}{100}$ x T x 120000 = 400 x 352 x $\frac{168}{100}$

⇒ $\frac{8279040000}{70000}$ x T = $\frac{23654400}{100}$

⇒ 118272 x T = 236544

⇒ T = 236544/ 118272

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

264cm

D=84cm

300m

126cm

speed

\frac{90km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 90 km / hr

= 90000m / hr

Diameter of the pipe,

= 2 r = 84 cm

Thus, r = $\frac{42}{100}$ m

Let h be the water level to be raised.

Thus, h = 126cm = $\frac{126}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 90000 m³

= $\frac{22}{7}$ x $\frac{42}{100}$ x $\frac{42}{100}$ x 90000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 300 x 264 x $\frac{126}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{42}{100}$ )² x T x 90000 = 300 x 264 x $\frac{126}{100}$

⇒ $\frac{22}{7}$ x $\frac{42}{100}$ x $\frac{42}{100}$ x T x 90000 = 300 x 264 x $\frac{126}{100}$

⇒ $\frac{3492720000}{70000}$ x T = $\frac{9979200}{100}$

⇒ 49896 x T = 99792

⇒ T = 99792/ 49896

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

220cm

D=70cm

250m

105cm

speed

\frac{75km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 75 km / hr

= 75000m / hr

Diameter of the pipe,

= 2 r = 70 cm

Thus, r = $\frac{35}{100}$ m

Let h be the water level to be raised.

Thus, h = 105cm = $\frac{105}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 75000 m³

= $\frac{22}{7}$ x $\frac{35}{100}$ x $\frac{35}{100}$ x 75000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 250 x 220 x $\frac{105}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{35}{100}$ )² x T x 75000 = 250 x 220 x $\frac{105}{100}$

⇒ $\frac{22}{7}$ x $\frac{35}{100}$ x $\frac{35}{100}$ x T x 75000 = 250 x 220 x $\frac{105}{100}$

⇒ $\frac{2021250000}{70000}$ x T = $\frac{5775000}{100}$

⇒ 28875 x T = 57750

⇒ T = 57750/ 28875

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

396cm

D=126cm

450m

189cm

speed

\frac{135km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 135 km / hr

= 135000m / hr

Diameter of the pipe,

= 2 r = 126 cm

Thus, r = $\frac{63}{100}$ m

Let h be the water level to be raised.

Thus, h = 189cm = $\frac{189}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 135000 m³

= $\frac{22}{7}$ x $\frac{63}{100}$ x $\frac{63}{100}$ x 135000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 450 x 396 x $\frac{189}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{63}{100}$ )² x T x 135000 = 450 x 396 x $\frac{189}{100}$

⇒ $\frac{22}{7}$ x $\frac{63}{100}$ x $\frac{63}{100}$ x T x 135000 = 450 x 396 x $\frac{189}{100}$

⇒ $\frac{11787930000}{70000}$ x T = $\frac{33679800}{100}$

⇒ 168399 x T = 336798

⇒ T = 336798/ 168399

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.

10)

396cm

D=126cm

450m

189cm

speed

\frac{135km}{hr}

it will take Answer: 2 hours to raise the required water level.

SOLUTION 1 :

Speed of water = 135 km / hr

= 135000m / hr

Diameter of the pipe,

= 2 r = 126 cm

Thus, r = $\frac{63}{100}$ m

Let h be the water level to be raised.

Thus, h = 189cm = $\frac{189}{100}$ m

Now, the volume of water discharged

= cross section area of the pipe x time x speed

= πr²x 1 x 135000 m³

= $\frac{22}{7}$ x $\frac{63}{100}$ x $\frac{63}{100}$ x 135000 m³

Volume of required quantity of water in the tank is,

Volume of rectangle = lbh

= 450 x 396 x $\frac{189}{100}$

Assume that T hours are needed to get the required quantity of water.

Volume of water discharged in T hours

= Required quantity of water in the tank

⇒ $\frac{22}{7}$ x ( $\frac{63}{100}$ )² x T x 135000 = 450 x 396 x $\frac{189}{100}$

⇒ $\frac{22}{7}$ x $\frac{63}{100}$ x $\frac{63}{100}$ x T x 135000 = 450 x 396 x $\frac{189}{100}$

⇒ $\frac{11787930000}{70000}$ x T = $\frac{33679800}{100}$

⇒ 168399 x T = 336798

⇒ T = 336798/ 168399

Thus, T = 2 hours.

Hence, it will take 2 hours to raise the required water level.