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 30m. 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)

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 64m. Diameter of the base is 30m . 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

64m

30m

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 38m . and height of the cylinder is 27m. 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)

27m

64m

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 36m. Diameter of the base is 34m . 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

36m

34m

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 38m . 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

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 49m. Diameter of the base is 38m . and height of the cylinder is 27m. 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)

27m

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 42m . and height of the cylinder is 15m. 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)

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 36m. Diameter of the base is 36m . 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

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 24m. 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)

24m

36m

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 36m. Diameter of the base is 48m . and height of the cylinder is 21m. 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)

21m

36m

48m

Answer:_______________

30m

81m

36m

Answer: 83301

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 = 15.50

Thus, the total cost of the canvas = 5374.29 x 15.50 = 83301.

15m

64m

30m

Answer: 32175

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 30m

Radius, r = 15m

Height, (h) = 15m

Conical Part :

Radius, r = 15m

Height, h₁ = 64 - 15 = 49m

Slant height, l = √ h₁²+ r²

√ 49² + 15²

=√ 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 15 x ( 2 x 15 + 35)

= $\frac{22}{7}$ x 15 x 65

= $\frac{21450}{7}$

Area of the canvas= 3064.29m²

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

Thus, the total cost of the canvas = 3064.29 x 10.50 = 32175.

27m

64m

38m

Answer: 66432

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 38m

Radius, r = 19m

Height, (h) = 27m

Conical Part :

Radius, r = 19m

Height, h₁ = 64 - 19 = 45m

Slant height, l = √ h₁²+ r²

√ 45² + 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 27 + 35)

= $\frac{22}{7}$ x 19 x 89

= $\frac{37202}{7}$

Area of the canvas= 5314.57m²

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

Thus, the total cost of the canvas = 5314.57 x 12.50 = 66432.

24m

36m

34m

Answer: 46563

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 34m

Radius, r = 17m

Height, (h) = 24m

Conical Part :

Radius, r = 17m

Height, h₁ = 36 - 17 = 19m

Slant height, l = √ h₁²+ r²

√ 19² + 17²

=√ 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 17 x ( 2 x 24 + 35)

= $\frac{22}{7}$ x 17 x 83

= $\frac{31042}{7}$

Area of the canvas= 4434.57m²

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

Thus, the total cost of the canvas = 4434.57 x 10.50 = 46563.

18m

49m

38m

Answer: 61476

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 = 14.50

Thus, the total cost of the canvas = 4239.71 x 14.50 = 61476.

27m

49m

38m

Answer: 82376

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 38m

Radius, r = 19m

Height, (h) = 27m

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 27 + 35)

= $\frac{22}{7}$ x 19 x 89

= $\frac{37202}{7}$

Area of the canvas= 5314.57m²

Now, the cost of canvas per Sq.m = 15.50

Thus, the total cost of the canvas = 5314.57 x 15.50 = 82376.

15m

81m

42m

Answer: 53625

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 = 12.50

Thus, the total cost of the canvas = 4290.00 x 12.50 = 53625.

18m

36m

Answer: 42174

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 36m

Radius, r = 18m

Height, (h) = 18m

Conical Part :

Radius, r = 18m

Height, h₁ = 36 - 18 = 18m

Slant height, l = √ h₁²+ r²

√ 18² + 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 18 + 35)

= $\frac{22}{7}$ x 18 x 71

= $\frac{28116}{7}$

Area of the canvas= 4016.57m²

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

Thus, the total cost of the canvas = 4016.57 x 10.50 = 42174.

24m

36m

32m

Answer: 60519

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 32m

Radius, r = 16m

Height, (h) = 24m

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 24 + 35)

= $\frac{22}{7}$ x 16 x 83

= $\frac{29216}{7}$

Area of the canvas= 4173.71m²

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

Thus, the total cost of the canvas = 4173.71 x 14.50 = 60519.

10)

21m

36m

48m

Answer: 66792

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 48m

Radius, r = 24m

Height, (h) = 21m

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 21 + 35)

= $\frac{22}{7}$ x 24 x 77

= $\frac{40656}{7}$

Area of the canvas= 5808.00m²

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

Thus, the total cost of the canvas = 5808.00 x 11.50 = 66792.