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 64m. Diameter of the base is 34m . 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

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 44m . and height of the cylinder is 27m. 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)

27m

49m

44m

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 50m . and height of the cylinder is 15m. 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)

15m

64m

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 36m. Diameter of the base is 30m . and height of the cylinder is 30m. 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)

30m

36m

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 32m . 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

64m

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 81m. 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

81m

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 36m . and height of the cylinder is 15m. 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)

15m

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 42m . and height of the cylinder is 21m. 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)

21m

49m

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 44m . and height of the cylinder is 18m. 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)

18m

81m

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 64m. 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

64m

46m

Answer:_______________

18m

64m

34m

Answer: 55005

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 34m

Radius, r = 17m

Height, (h) = 18m

Conical Part :

Radius, r = 17m

Height, h₁ = 64 - 17 = 47m

Slant height, l = √ h₁²+ r²

√ 47² + 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 18 + 35)

= $\frac{22}{7}$ x 17 x 71

= $\frac{26554}{7}$

Area of the canvas= 3793.43m²

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

Thus, the total cost of the canvas = 3793.43 x 14.50 = 55005.

27m

49m

44m

Answer: 89229

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 44m

Radius, r = 22m

Height, (h) = 27m

Conical Part :

Radius, r = 22m

Height, h₁ = 49 - 22 = 27m

Slant height, l = √ h₁²+ r²

√ 27² + 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 27 + 35)

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

= $\frac{43076}{7}$

Area of the canvas= 6153.71m²

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

Thus, the total cost of the canvas = 6153.71 x 14.50 = 89229.

15m

64m

50m

Answer: 68946

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 50m

Radius, r = 25m

Height, (h) = 15m

Conical Part :

Radius, r = 25m

Height, h₁ = 64 - 25 = 39m

Slant height, l = √ h₁²+ r²

√ 39² + 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 15 + 35)

= $\frac{22}{7}$ x 25 x 65

= $\frac{35750}{7}$

Area of the canvas= 5107.14m²

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

Thus, the total cost of the canvas = 5107.14 x 13.50 = 68946.

30m

36m

30m

Answer: 51504

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 30m

Radius, r = 15m

Height, (h) = 30m

Conical Part :

Radius, r = 15m

Height, h₁ = 36 - 15 = 21m

Slant height, l = √ h₁²+ r²

√ 21² + 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 30 + 35)

= $\frac{22}{7}$ x 15 x 95

= $\frac{31350}{7}$

Area of the canvas= 4478.57m²

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

Thus, the total cost of the canvas = 4478.57 x 11.50 = 51504.

24m

64m

32m

Answer: 47998

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 32m

Radius, r = 16m

Height, (h) = 24m

Conical Part :

Radius, r = 16m

Height, h₁ = 64 - 16 = 48m

Slant height, l = √ h₁²+ r²

√ 48² + 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 = 11.50

Thus, the total cost of the canvas = 4173.71 x 11.50 = 47998.

27m

81m

38m

Answer: 66432

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 38m

Radius, r = 19m

Height, (h) = 27m

Conical Part :

Radius, r = 19m

Height, h₁ = 81 - 19 = 62m

Slant height, l = √ h₁²+ r²

√ 62² + 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.

15m

36m

Answer: 49641

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 36m

Radius, r = 18m

Height, (h) = 15m

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 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 = 13.50

Thus, the total cost of the canvas = 3677.14 x 13.50 = 49641.

21m

49m

42m

Answer: 73689

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 42m

Radius, r = 21m

Height, (h) = 21m

Conical Part :

Radius, r = 21m

Height, h₁ = 49 - 21 = 28m

Slant height, l = √ h₁²+ r²

√ 28² + 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 21 + 35)

= $\frac{22}{7}$ x 21 x 77

= $\frac{35574}{7}$

Area of the canvas= 5082.00m²

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

Thus, the total cost of the canvas = 5082.00 x 14.50 = 73689.

18m

81m

44m

Answer: 56455

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 44m

Radius, r = 22m

Height, (h) = 18m

Conical Part :

Radius, r = 22m

Height, h₁ = 81 - 22 = 59m

Slant height, l = √ h₁²+ r²

√ 59² + 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 18 + 35)

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

= $\frac{34364}{7}$

Area of the canvas= 4909.14m²

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

Thus, the total cost of the canvas = 4909.14 x 11.50 = 56455.

10)

24m

64m

46m

Answer: 80996

SOLUTION 1 :

Cylindrical part

Diameter, 2r = 46m

Radius, r = 23m

Height, (h) = 24m

Conical Part :

Radius, r = 23m

Height, h₁ = 64 - 23 = 41m

Slant height, l = √ h₁²+ r²

√ 41² + 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.