Geometry

Solids

Medium

Consider the surface area of the following solids.

(A) A cube of edge 8 cm.

(B) A cylinder with a diameter of base 10 cm and height 42 cm.

(C) A hemisphere with 14 cm diameter.

(D) A sphere with a radius 21 cm.

Arrange the above in decreasing order.

Choose the correct answer from the options given below:

(C), (A), (B), (D)

(A), (C), (D), (B)

(D), (B), (C), (A)

(D), (B), (A), (C)

✅ Correct Option: 4

There is an ambiguity in the question.

Using curved surface area for the cylinder and hemisphere:

Solid	Surface area	Value
(A) Cube	$6a^2$	$6(8)^2 = 384$ cm²
(B) Cylinder	$2\pi rh$	$2\pi(5)(42) = 420\pi \approx 1320$ cm²
(C) Hemisphere	$2\pi r^2$	$2\pi(7)^2 = 98\pi \approx 308$ cm²
(D) Sphere	$4\pi r^2$	$4\pi(21)^2 = 1764\pi \approx 5544$ cm²

Therefore,

$D > B > A > C$ (which is what NTA's answer key says).

However, if “surface area” means total surface area, then the hemisphere has $3\pi r^2 = 147\pi \approx 462$ cm², making the order D > B > C > A (Option 3).

The question should ideally specify whether curved or total surface area is required. Sigh, NTA at it again!

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2025: 30 May Shift 2

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2023: 5 June Shift 2

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Solution

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