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 81m. 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 15.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

15m

81m

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 64m. Diameter of the base is 40m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 14.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

64m

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 81m. Diameter of the base is 42m . and height of the cylinder is 15m. 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)

15m

81m

42m

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 36m . and height of the cylinder is 30m. Find the cost of canvas needed to make the tent, if the cost of canvas is 14.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

30m

81m

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 50m . and height of the cylinder is 24m. 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)

24m

49m

50m

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 48m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 15.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

64m

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 81m. Diameter of the base is 36m . and height of the cylinder is 24m. 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)

24m

81m

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 36m. Diameter of the base is 32m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 14.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

36m

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 32m . and height of the cylinder is 18m. Find the cost of canvas needed to make the tent, if the cost of canvas is 14.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

18m

49m

32m

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 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 14.50/ m2. (take π = $\frac{22}{7}$ ) (write answer the nearest round number)

15m

49m

36m

Answer:_______________

15m

81m

36m

Answer: 56996

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 36m

Radius, r = 18m

Height, (h) = 15m

Conical Part :

Radius, r = 18m

Height, h₁ = 81 - 18 = 63m

Slant height, l = √ h₁²+ r²

√ 63² + 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 = 15.50

Thus, the total cost of the canvas = 3677.14 x 15.50 = 56996.

18m

64m

40m

Answer: 64711

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 40m

Radius, r = 20m

Height, (h) = 18m

Conical Part :

Radius, r = 20m

Height, h₁ = 64 - 20 = 44m

Slant height, l = √ h₁²+ r²

√ 44² + 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 18 + 35)

= $\frac{22}{7}$ x 20 x 71

= $\frac{31240}{7}$

Area of the canvas= 4462.86m²

Now, the cost of canvas per Sq.m = 14.50

Thus, the total cost of the canvas = 4462.86 x 14.50 = 64711.

15m

81m

42m

Answer: 45045

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 42m

Radius, r = 21m

Height, (h) = 15m

Conical Part :

Radius, r = 21m

Height, h₁ = 81 - 21 = 60m

Slant height, l = √ h₁²+ r²

√ 60² + 21²

=√ 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 21 x ( 2 x 15 + 35)

= $\frac{22}{7}$ x 21 x 65

= $\frac{30030}{7}$

Area of the canvas= 4290.00m²

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

Thus, the total cost of the canvas = 4290.00 x 10.50 = 45045.

30m

81m

36m

Answer: 77927

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 36m

Radius, r = 18m

Height, (h) = 30m

Conical Part :

Radius, r = 18m

Height, h₁ = 81 - 18 = 63m

Slant height, l = √ h₁²+ r²

√ 63² + 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 30 + 35)

= $\frac{22}{7}$ x 18 x 95

= $\frac{37620}{7}$

Area of the canvas= 5374.29m²

Now, the cost of canvas per Sq.m = 14.50

Thus, the total cost of the canvas = 5374.29 x 14.50 = 77927.

24m

49m

50m

Answer: 81518

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 50m

Radius, r = 25m

Height, (h) = 24m

Conical Part :

Radius, r = 25m

Height, h₁ = 49 - 25 = 24m

Slant height, l = √ h₁²+ r²

√ 24² + 25²

=√ 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 25 x ( 2 x 24 + 35)

= $\frac{22}{7}$ x 25 x 83

= $\frac{45650}{7}$

Area of the canvas= 6521.43m²

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

Thus, the total cost of the canvas = 6521.43 x 12.50 = 81518.

18m

64m

48m

Answer: 83009

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 48m

Radius, r = 24m

Height, (h) = 18m

Conical Part :

Radius, r = 24m

Height, h₁ = 64 - 24 = 40m

Slant height, l = √ h₁²+ r²

√ 40² + 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 = 15.50

Thus, the total cost of the canvas = 5355.43 x 15.50 = 83009.

24m

81m

36m

Answer: 53997

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 36m

Radius, r = 18m

Height, (h) = 24m

Conical Part :

Radius, r = 18m

Height, h₁ = 81 - 18 = 63m

Slant height, l = √ h₁²+ r²

√ 63² + 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 24 + 35)

= $\frac{22}{7}$ x 18 x 83

= $\frac{32868}{7}$

Area of the canvas= 4695.43m²

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

Thus, the total cost of the canvas = 4695.43 x 11.50 = 53997.

18m

36m

32m

Answer: 51769

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 32m

Radius, r = 16m

Height, (h) = 18m

Conical Part :

Radius, r = 16m

Height, h₁ = 36 - 16 = 20m

Slant height, l = √ h₁²+ r²

√ 20² + 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 18 + 35)

= $\frac{22}{7}$ x 16 x 71

= $\frac{24992}{7}$

Area of the canvas= 3570.29m²

Now, the cost of canvas per Sq.m = 14.50

Thus, the total cost of the canvas = 3570.29 x 14.50 = 51769.

18m

49m

32m

Answer: 51769

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 32m

Radius, r = 16m

Height, (h) = 18m

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 18 + 35)

= $\frac{22}{7}$ x 16 x 71

= $\frac{24992}{7}$

Area of the canvas= 3570.29m²

Now, the cost of canvas per Sq.m = 14.50

Thus, the total cost of the canvas = 3570.29 x 14.50 = 51769.

10)

15m

49m

36m

Answer: 53319

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 = 14.50

Thus, the total cost of the canvas = 3677.14 x 14.50 = 53319.