Mensuration — 2D & 3D — Practice

Question 1

The area of a circle is 154 cm². Its circumference is:
(a) 22 cm  (b) 44 cm  (c) 49 cm  (d) 88 cm

Accepted Answer

(22/7)r² = 154 ⇒ r² = 49 ⇒ r = 7; circumference = 2πr = 44.

Answer: (b) 44 cm.

Question 2

A 20 m × 15 m field is fenced at ₹10 per metre. The cost is:
(a) ₹600  (b) ₹700  (c) ₹3000  (d) ₹350

Accepted Answer

Perimeter = 2(20+15) = 70 m; cost = 70 × 10 = ₹700.

Answer: (b) ₹700.

Question 3

A cylinder of radius 7 cm and height 10 cm has volume:
(a) 1540 cm³  (b) 440 cm³  (c) 2200 cm³  (d) 1078 cm³

Accepted Answer

πr²h = (22/7)×49×10 = 1540.

Answer: (a) 1540 cm³.

Question 4

A sphere of radius 6 cm is melted into small spheres of radius 3 cm. Number formed:
(a) 2  (b) 4  (c) 8  (d) 16

Accepted Answer

6³/3³ = 216/27 = 8 (volume conserved).

Answer: (c) 8.

Question 5

If a cube's edge increases by 50%, its volume increases by:
(a) 150%  (b) 225%  (c) 237.5%  (d) 337.5%

Accepted Answer

Volume ×(1.5)³ = 3.375 ⇒ 237.5% increase.

Answer: (c) 237.5%.

Question 6

The curved surface area of a cone with radius 7 cm and slant height 10 cm is:
(a) 220 cm²  (b) 154 cm²  (c) 374 cm²  (d) 210 cm²

Accepted Answer

Curved = πrl = (22/7)×7×10 = 220.

Answer: (a) 220 cm².

Practice — Mensuration — 2D & 3D