# Mensuration - 3D

1. Find the total surface area of a spherical ball of radius 9 cm. [Use π = 3.14]

A) 1017 cm2 B) 874 cm2 C) 946 cm2 D) 1020 cm2

Explanation: Total surface area of sphere = 4πr 2 Here r is the radius.

= 4 × 3.14 × 92 = 1017 cm2

Ans: A

2. The ratio of height and radius of a cylinder is 3 : 1, respectively. If curved surface area of cylinder is 678 cm2, then find the height of cylinder. [Take π = 3.14]

A) 18 cm B) 12 cm C) 14 cm D) 15 cm

Explanation: Let, height and radius of the cylinder be ‘3x’cm and ‘x’ cm, respectively. So, (2 × 3.14 × 3)x2 = 678  x = √ 36 = 6 So, height of cylinder = 3x = 18 cm

Ans: A

3. What is the volume of a right circular cone whose height is 20 m and radius is one fourth of its height? [Use π = 3.14]

A) 420 m3 B) 523 m3 C) 540 m3 D) 660 m3

where r is the radius and h is the height of cone.

Ans: B

4. Find the radius of the solid hemisphere of volume 6,750 m3. (Take π = 3)

A) 12 m     B) 14 m   C) 15 m    D) 16 m

5. The height, breadth and length of a cuboidal box are 18 cm, ‘x’ cm and 42 cm, respectively. If the cost of painting the base of the box was Rs.1449 at Rs.1.50 per cm2, then find the value of ‘x’.

A) 23 cm     B)19 cm     C) 27 cm      D) 26 cm

Explanation: Area of the base = l × b 1449

42x = 966

So, x = 23 cm

Ans: A

6. If the radius and height of a cylinder is decreased by 20% and 25%, respectively. Find the percentage decrease in the volume of the cylinder.

A) 52%     B) 46%    C) 54%     D) 58%

Explanation: Let, radius and height of cylinder be ‘r’ and ‘h’, respectively.

Decreased height = 0.75h

So, original volume = πr2h

Decreased volume = π × (0.8r)2 × 0.75h = 0.48 πr2h

So, required percentage

= 52%

Ans: A

7. Find the cost of painting a solid cylindrical drum having radius 14 meters and height 20 meters at the rate of Rs.15 per square meter.

A) Rs. 42,680 B) Rs. 44,880 C) Rs. 46,080 D) None of these

Explanation: Total surface area of cylinder = 2 × π × r × (h + r)

= 88 × 34 = 2992 m2

So the cost of painting

= 2992 × 15 = Rs. 44,880

Ans: B

8. Breadth of the cuboidal box is half its length and one fifth its height. Find the lateral surface area of the cuboidal box if its volume is 58,320 cm2

A) 11,016 cm2 B) 10,208 cm2 C) 9,720 cm2 D) None of these

Explanation: Let the cuboidal box breadth = x cm, length = 2x cm, height = 5x cm So the volume of the box

= x × 2x × 5x = 58320 10x3 = 58320

x3 = 5832 ⇒ x = 18 So the length, breadth and the height of the box are 36 cm, 18 cm and 90 cm respectively. So the lateral surface area of the box

= 2 × 90 × (18 + 36) = 9,720 cm2

Ans: C

9. A cone of radius 22 cm and height 33 cm is melted and casted in form of a cylinder of equal base, then find the height of cylinder.

A) 33 cm B) 22 cm C) 11 cm D) None of these

Explanation: Let ‘r’, ‘h’ and ‘H’ denote the radius of the cone, height of the cone and height of the cylinder respectively. According to question, volume of cone

H = 11 cm

Ans: C

10. Find the cost of painting the total surface area of the hemisphere of radius 14 m at the rate of Rs.12.50/ m2.

A) Rs. 23,100 B) Rs. 21,140 C) Rs. 22,220 D) None of these

Explanation: Total surface area of the hemisphere

So, required cost of painting = 1848 × 12.50 = Rs. 23,100

Ans: A

11. The height and radius of base of the right circular cone are in the ratio 4 : 3 respectively. If the curved surface area of the cone is 2310 cm2, then find the difference in the diameter and height of the cone.

A) 28 cm     B) 14 cm    C) 7 cm    D) None of these

Explanation: Let the radius of base and the height of the cone be ‘3x’ cm and ‘4x’ cm respectively

So, the slant height of the cone

So, the curved surface area of the cone

15x2 = 735 x2 = 49 x = 7

So, the radius and height of the cone are 21 cm and 28 cm respectively. Desired difference = 21 × 2 − 28 = 14 cm

Ans: B

12. A hollow cylinder of height 25 cm is unwrapped to get a rectangle of dimensions 88 cm × 25 cm. Find the volume of the cylinder.

A) 12600 cm3 B) 15400 cm3 C) 16400 cm3 D) 14800 cm3

Explanation: When a hollow cylinder is unwrapped, Breadth of the rectangle = Height of the cylinder. So, height of cylinder

= 25 cm Also, length of the rectangle

= circumference of base of the cylinder

r = 14 cm

Thus, volume of the cylinde

= 15400 cm

Ans: B

13. Find the curved surface area of the cone of radius 5 cm and height equal to the breadth of the rectangle of area 180 cm2 whose length and breadth are in the ratio of 5 : 4, respectively. [Use π = 3.14]

A) 204 cm2   B) 210 cm2   C) 184 cm2   D) None of these

Explanation: Let the length and breadth of the rectangle be‘5x’ cm and ‘4x’ cm, respectively. According to question, 5x × 4x = 180

20x2 = 180

x2 = 9

x = 3

So, breadth of rectangle = 4x = 12 cm Curved surface area of the cone = π × 5 × (122 + 52)0.5 = 3.14 × 5 × 13 = 204 cm2

Ans: A

14. A cylinder of radius 8 cm and height 16 cm is melted and again cast to form small cylinders of radius 2 cm and height 4 cm. Find the number of small cylinders that can be formed from the big cylinder.

A) 42   B) 64   C) 36   D) 48

Explanation: Required number of cylinders that can be formed

Ans: B

15. If the volume of the sphere is 38808 m3, then find the total surface area of the sphere.

A) 5372 m B) 5544 m2  C) 5648 m D) 5775 m2

Explanation: Let the radius of the sphere be ‘r’ meters. Volume of the sphere = 38808

r3 = 9261

r = 21 m

So, the total surface area of the sphere

Ans: B

16. The total surface area of the cylinder is 1104 cm2 If the cost of painting the curved surface area of the cylinder is Rs. 2520 at the rate of Rs. 3.5/cm2, then find the radius of the cylinder. [Use π = 3]

A) 12 cm   B) 7 cm   C) 9 cm   D) 8

Explanation: Total surface area of the cylinder = 1104 cm2 Curved surface area of the cylinder

So, 2πrh + 2πr2 − 2πrh = 1104 − 720

2πr2 = 384

r = 8

cm So, the radius of the cylinder is 8 cm

Ans: D

17. A toy which is in the form of hemispheres mounted on both ends of a hollow cylinder such that their bases coincide. If the length of the toy is 20 cm and the total curved surface area of the toy is 572 cm2, then find the height of the cylinder.

A) 8.8 cm B) 10.9 cm C) 9.1 cm D) 9 cm

Explanation: Let the radius of the cylinder (or hemisphere) be ‘r’ cm and the height of the cylinder be ‘h’ cm.

Then, 2r + h = 20 ⇒ h = 20 − 2r

Also, total CSA of the toy = 572 cm2

2 × π × r2 + 2 × π × r × h + 2 × π × r2 = 572

4 × π × r2 + 2 × π × r × (20 − 2r) = 572

4 × π × r2 + 40 × π × r − 4 × π× r2 = 572

r = 4.55 cm

Thus, height of the cylinder = 20 − 2 × 4.55 = 10.9 cm

Ans: B

Posted Date : 31-07-2023

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