Sasi Math (Revised for 1024)

Scroll:Mensuration >> circumference of cylinder and cone >> ps (4133)

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.

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 49m. Diameter of the base is 38m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 12.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

49m

38m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 81m. Diameter of the base is 32m . and height of the cylinder is 21m. Find the cost of canvas needed to make the tent, if the cost of canvas is 12.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

21m

81m

32m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 36m. Diameter of the base is 46m . and height of the cylinder is 24m. Find the cost of canvas needed to make the tent, if the cost of canvas is 13.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

24m

36m

46m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 49m. Diameter of the base is 40m . and height of the cylinder is 24m. Find the cost of canvas needed to make the tent, if the cost of canvas is 13.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

24m

49m

40m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 49m. Diameter of the base is 32m . and height of the cylinder is 27m. Find the cost of canvas needed to make the tent, if the cost of canvas is 13.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

27m

49m

32m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 49m. Diameter of the base is 36m . and height of the cylinder is 15m. Find the cost of canvas needed to make the tent, if the cost of canvas is 11.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

15m

49m

36m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 49m. Diameter of the base is 48m . and height of the cylinder is 24m. Find the cost of canvas needed to make the tent, if the cost of canvas is 10.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

24m

49m

48m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 36m. Diameter of the base is 38m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 10.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

36m

38m

Answer:_______________

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 64m. Diameter of the base is 44m . and height of the cylinder is 30m. Find the cost of canvas needed to make the tent, if the cost of canvas is 10.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

30m

64m

44m

Answer:_______________

10)

A circus tent is to be erected in the form in the from of a cone surmounted on a cylinder. The total height of the tent is 36m. Diameter of the base is 48m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 12.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

36m

48m

Answer:_______________

18m

49m

38m

Answer: 52996

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 38m

Radius, r = 19m

Height, (h) = 18m

Conical Part :

Radius, r = 19m

Height, h₁ = 49 - 19 = 30m

Slant height, l = √ h₁²+ r²

√ 30² + 19²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 19 x ( 2 x 18 + 35)

= $\frac{22}{7}$ x 19 x 71

= $\frac{29678}{7}$

Area of the canvas= 4239.71m²

Now, the cost of canvas per Sq.m = 12.50

Thus, the total cost of the canvas = 4239.71 x 12.50 = 52996.

21m

81m

32m

Answer: 48400

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 32m

Radius, r = 16m

Height, (h) = 21m

Conical Part :

Radius, r = 16m

Height, h₁ = 81 - 16 = 65m

Slant height, l = √ h₁²+ r²

√ 65² + 16²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 16 x ( 2 x 21 + 35)

= $\frac{22}{7}$ x 16 x 77

= $\frac{27104}{7}$

Area of the canvas= 3872.00m²

Now, the cost of canvas per Sq.m = 12.50

Thus, the total cost of the canvas = 3872.00 x 12.50 = 48400.

24m

36m

46m

Answer: 80996

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 46m

Radius, r = 23m

Height, (h) = 24m

Conical Part :

Radius, r = 23m

Height, h₁ = 36 - 23 = 13m

Slant height, l = √ h₁²+ r²

√ 13² + 23²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 23 x ( 2 x 24 + 35)

= $\frac{22}{7}$ x 23 x 83

= $\frac{41998}{7}$

Area of the canvas= 5999.71m²

Now, the cost of canvas per Sq.m = 13.50

Thus, the total cost of the canvas = 5999.71 x 13.50 = 80996.

24m

49m

40m

Answer: 70431

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 40m

Radius, r = 20m

Height, (h) = 24m

Conical Part :

Radius, r = 20m

Height, h₁ = 49 - 20 = 29m

Slant height, l = √ h₁²+ r²

√ 29² + 20²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 20 x ( 2 x 24 + 35)

= $\frac{22}{7}$ x 20 x 83

= $\frac{36520}{7}$

Area of the canvas= 5217.14m²

Now, the cost of canvas per Sq.m = 13.50

Thus, the total cost of the canvas = 5217.14 x 13.50 = 70431.

27m

49m

32m

Answer: 60418

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 32m

Radius, r = 16m

Height, (h) = 27m

Conical Part :

Radius, r = 16m

Height, h₁ = 49 - 16 = 33m

Slant height, l = √ h₁²+ r²

√ 33² + 16²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 16 x ( 2 x 27 + 35)

= $\frac{22}{7}$ x 16 x 89

= $\frac{31328}{7}$

Area of the canvas= 4475.43m²

Now, the cost of canvas per Sq.m = 13.50

Thus, the total cost of the canvas = 4475.43 x 13.50 = 60418.

15m

49m

36m

Answer: 42287

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 36m

Radius, r = 18m

Height, (h) = 15m

Conical Part :

Radius, r = 18m

Height, h₁ = 49 - 18 = 31m

Slant height, l = √ h₁²+ r²

√ 31² + 18²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 18 x ( 2 x 15 + 35)

= $\frac{22}{7}$ x 18 x 65

= $\frac{25740}{7}$

Area of the canvas= 3677.14m²

Now, the cost of canvas per Sq.m = 11.50

Thus, the total cost of the canvas = 3677.14 x 11.50 = 42287.

24m

49m

48m

Answer: 65736

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 48m

Radius, r = 24m

Height, (h) = 24m

Conical Part :

Radius, r = 24m

Height, h₁ = 49 - 24 = 25m

Slant height, l = √ h₁²+ r²

√ 25² + 24²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 24 x ( 2 x 24 + 35)

= $\frac{22}{7}$ x 24 x 83

= $\frac{43824}{7}$

Area of the canvas= 6260.57m²

Now, the cost of canvas per Sq.m = 10.50

Thus, the total cost of the canvas = 6260.57 x 10.50 = 65736.

18m

36m

38m

Answer: 44517

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 38m

Radius, r = 19m

Height, (h) = 18m

Conical Part :

Radius, r = 19m

Height, h₁ = 36 - 19 = 17m

Slant height, l = √ h₁²+ r²

√ 17² + 19²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 19 x ( 2 x 18 + 35)

= $\frac{22}{7}$ x 19 x 71

= $\frac{29678}{7}$

Area of the canvas= 4239.71m²

Now, the cost of canvas per Sq.m = 10.50

Thus, the total cost of the canvas = 4239.71 x 10.50 = 44517.

30m

64m

44m

Answer: 68970

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 44m

Radius, r = 22m

Height, (h) = 30m

Conical Part :

Radius, r = 22m

Height, h₁ = 64 - 22 = 42m

Slant height, l = √ h₁²+ r²

√ 42² + 22²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 22 x ( 2 x 30 + 35)

= $\frac{22}{7}$ x 22 x 95

= $\frac{45980}{7}$

Area of the canvas= 6568.57m²

Now, the cost of canvas per Sq.m = 10.50

Thus, the total cost of the canvas = 6568.57 x 10.50 = 68970.

10)

18m

36m

48m

Answer: 66943

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 48m

Radius, r = 24m

Height, (h) = 18m

Conical Part :

Radius, r = 24m

Height, h₁ = 36 - 24 = 12m

Slant height, l = √ h₁²+ r²

√ 12² + 24²

=√ 784 + 441

= √ 1225 = 35m.

Total area or the canvas needed

= CSA of the cylindrical part + CSA of the conical part

= 2πrh + πrl = πr(2h + l)

= $\frac{22}{7}$ x 24 x ( 2 x 18 + 35)

= $\frac{22}{7}$ x 24 x 71

= $\frac{37488}{7}$

Area of the canvas= 5355.43m²

Now, the cost of canvas per Sq.m = 12.50

Thus, the total cost of the canvas = 5355.43 x 12.50 = 66943.