Mensuration Questions for Clerk Mains Exam

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1) If the ratio of the radius of the cone to cylinder is 1: 2 and the slanting height of the cone is 25 cm. The surface area of the cone is equal to the total surface area of the sphere whose radius is 2√14 cm. If the height of the cylinder is equal to the height of the cone, then what is the curved surface area of the cylinder?

A.2612 cm²

B.2412 cm²

C.2012 cm²

D.2112 cm²

E.None of these

2) If the circumference of the circle is 44 cm and the radius of the cone is equal to the radius of the circle. The Curved surface area of the cone is 550 cm² and the ratio of the height of the cone to height of the cylinder is 4:3. If the ratio of the radius of the cylinder to cone is 1:2, then what is the volume of the cylinder?

A.663 cm³

B.673 cm³

C.683 cm³

D.693 cm³

E.None of these

3) If the radius of circle is 7 cm and ratio of the diameter of the circle to length of the rectangle is 1: 1, then the ratio of breadth of the rectangle to the side of the square 5: 8. If the sum of the area of circle and rectangle is 294 cm², then what is the difference between the perimeter of the rectangle and the perimeter of the square?

A.24 cm

B.14 cm

C.17 cm

D.16 cm

E.None of these

4) If the ratio of the radius to slanting height of the cone is 3:5 and volume of the cylinder is equal to the volume of the cone. If the radius of the cylinder is 4 cm and the height of the cylinder is equal to the side of the square whose perimeter is 192 cm, then what is the curved surface area of the cone?

A.90Π cm²

B.180Π cm²

C.240Π cm²

D.Cannot be determined

E.None of these

5) If the circumference of the circle is equal to the perimeter of the square and Length of the rectangle is 8 cm more than the side of the square. If the radius of the circle is equal to the side of the equilateral triangle whose perimeter is 42 cm and the breadth of the rectangle is 6 cm more than the side of the equilateral triangle, then what is the perimeter of the rectangle?

A.80 cm

B.90 cm

C.100 cm

D.120 cm

E.None of these

6) If the total cost of the leveling in the rectangle field is Rs.10800 at the rate of Rs.9 per square meter and the side of the square is 80% of the breadth of the rectangle. If the ratio of the length and breadth of the rectangle is 4:3, then what is the difference between the perimeter of the rectangle field and square?

A.22 m

B.33 m

C.44 m

D.55 m

E.None of these

7) Perimeter of a rectangle is x meter and circumference of a circle is 52 meter more than the perimeter of the rectangle. Ratio of radius of circle and length of the rectangle is 3: 4 and ratio of length and breadth of rectangle is 7: 3. Find the area of the rectangle?

A.418 Sq m

B.352 Sq m

C.336 Sq m

D.384 Sq m

E.None of these

8) If the volume of the cone is 1232 cm³ and the area of the rectangle is 360 cm² and the perimeter of the square is 60 cm. If the side of the square is equal to the breadth of the rectangle and the length of the rectangle is equal to the height of the cone, then what is the slanting height of the cone?

A.20 cm

B.22 cm

C.24 cm

D.18 cm

E.None of these

9) The radius and height of a cylinder are 15 cm and 20 cm respectively. If the radius is increased by ___ % and the height is increased by ___ %, the volume of the cylinder would increase by ___ %. Which of the following values can we fill in the same order?

(i) 25, 20, 87.5

(ii) 30, 10, 85

(iii) 10, 40, 70

(iv) 20, 25, 80

A.Only (iv)

B.Only (iii)

C.(i),(ii) and (iv)

D.Only (i) and (iv)

E.None follow

10) Area of the circle is 154 cm² and the radius of the cone is equal to the radius of the circle. Height of the cone is double of the height of the cylinder whose volume is 7392 cm³ and the curved surface area of the cone is 550 cm².

From the statement given in the above question which of the following can be determined.

a) Slanting height of the cone

b) Radius of the cylinder

c) Total surface area of the cylinder

d) If the radius of the cylinder is equal to the breadth of the rectangle whose perimeter is 68 cm, then find the area of the rectangle?

A.Only A

B.Only A and B

C.Only A, B and C

D.All A, B, C and D

E.None of these

 

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Answers :

1) Answer: D

Total Surface area of the sphere = 4 * 22/7 * r * r

= 4 * 22/7 * 2√14 * 2√14

= 704 cm²

Total Surface area of the cone = 22/7 * r * (l + r)

704 = 22/7 * r * (25 + r)

r = 7 cm

Radius of the cone = 7 cm

Height of the cone = √25² – 7² = 24 cm

Radius of the cylinder = 2/1 * 7 = 14 cm

Curved surface area of the cylinder = 2 * 22/7 * r * h

= 2 * 22/7 * 14 * 24 = 2112 cm²

2) Answer: D

Circumference of the circle = 2 * 22/7 * r

44 = 2 * 22/7 * r

Radius of the circle = 7 cm

Radius of the cone = 7 cm

CSA of the cone = 22/7 * r * l

550 = 22/7 * 7 * l

Slanting height of the cone = 25 cm

Height of the cone = √25² – 7² = 24 cm

Radius of the cylinder = ½ * 7 = 3.5 cm

Height of the cylinder = 3/4 * 24 = 18 cm

Volume of the cylinder = 22/7 * r * r * h

= 22/7 * 3.5 * 3.5 * 18 = 693 cm³

3) Answer: D

Area of the circle=22/7 * 7 * 7 = 154 cm²

Area of the rectangle = 294 – 154 = 140 cm²

Length * breadth = 140

Length of the rectangle = 14 cm

Breadth of the rectangle = 140/14 = 10 cm

Side of the square = 8/5 * 10 = 16 cm

Perimeter of the square = 4 * 16 = 64 cm

Perimeter of the rectangle = 2 * (l + b) = 2 * (14 + 10) = 48

Difference = 64 – 48 = 16 cm

4) Answer: C

Height of the cone = √(5x² – 3x²) = 4x

Volume of the cone = 1/3 * 22/7 * r² * h

Volume of the cylinder = 22/7 * r² * h

Side of the square = 192/4 = 48

Height of the cylinder = 48

1/3 * 22/7 * 3x * 3x * 4x = 22/7 * 4 * 4 * 48

x = 4 cm

Radius of the cone = 3 * 4 = 12 cm

Slating height of the cone = 5 * 4 = 20 cm

CSA of the cone = 22/7 * r * l

= 22/7 * 12 * 20 = 240Π cm²

5) Answer: C

Side of the equilateral triangle = 42/3 = 14 cm

Radius of the circle = 14 cm

Breadth of the rectangle = 14 + 6 = 20 cm

Circumference of the circle = 2 * 22/7 * 14 = 88 cm

Perimeter of the square = 4 * a = 88 cm

Side of the square a = 22 cm

Length of the rectangle = 22 + 8 = 30 cm

Perimeter of the rectangle = 2 * (l + b)

= 2 * (30 + 20) = 100 cm

6) Answer: C

Area of the rectangle = 10800/9 = 1200

4x * 3x = 1200

x = 10 m

Length of the rectangle = 40 m

Breadth of the rectangle= 30 m

Side of the square = 80/100 * 30 = 24 m

Perimeter of the square = 24 * 4 = 96 m

Perimeter of the rectangle = 2 * (40 + 30) = 140 m

Difference = 140 – 96 = 44 m

7) Answer: C

Perimeter of rectangle = 2 * (l + b) = x

2l + 2b = x and 2πr = x + 52

r/l = 3/4 and l/b = 7/3

r : l : b = 21 : 28 : 12 (21y, 28y, 12y)

2πr = x + 52

2πr = 2l + 2b + 52

πr = l + b + 26

(22/7) * 21y = 28y + 12y + 26

66y = 40y + 26

26y = 26

y = 1

Length of the rectangle = 28y = 28 m

Breadth of the rectangle = 12y = 12 m

The area of the rectangle = l * b = 28 * 12 = 336 Sq m

8) Answer: E

Side of the square = 60/4 = 15 cm

Breadth of the rectangle = 15 cm

Length of the rectangle = 360/15 = 24 cm

Height of the cone = 24 cm

1232 = 1/3 * 22/7 * r * r * 24

Radius of the cone = 7 cm

Slanting height of the cone = √ (24² + 7²)

= 25 cm

9) Answer: D

Suppose the radius of the cylinder is R and height is H.

Volume = πR²H

(i)
New volume = π(1.25 R)²(1.2 H) = 1.875 πR²H

Increase in volume = 87.5%

(ii)
New volume = π(1.3 R)²(1.1 H) = 1.859 πR²H

Increase in volume = 85.9%

(iii)
New volume = π(1.1 R)²(1.4 H) = 1.694 πR²H

Increase in volume = 69.4%

(iv)
New volume = π(1.2 R)²(1.25 H) = 1.8 πR²H

Increase in volume = 80%

Only (i) and (iv) satisfy the condition.

10) Answer: D

Area of the circle = 154 cm

22/7 * r * r = 154

Radius of the circle = 7 cm

550 = 22/7 * l * 7

Slanting height of the cone = 25 cm

Height of the cone = √25² – 7² = 24 cm

Height of the cylinder = 24/2 = 12 cm

7392 = 22/7 * R * R * 12

Radius of the cylinder = 14 cm

Total surface area of the cylinder = 2 * 22/7 * 14 * (12 + 14)

= 2288 cm²

2 * (14 + l) = 68

l = 20

Area of the rectangle = 20 * 14 = 280 cm²

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