Consider the surface area of the following:

(A) A cube having each side as 6 cm.

(B) A cylinder with a diameter of base 14 cm and length 80 cm.

(C) A cone of diameter 14 cm and a slant height of 10 cm.

(D) A sphere of radius 10.5 cm.

The surface area of these in decreasing order are:

Choose the correct answer from the options given below:

(A) Cube with side = 6 cm

Surface area of cube = 6 × (side)²

Surface area = 6 × 6²

$= 6 \times 36$

$= 216$ cm²

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(B) Cylinder with diameter = 14 cm, height = 80 cm

Total surface area = 2πr(r + h)

Radius (r) = 14 ÷ 2 = 7 cm

Height (h) = 80 cm

Using π = 22/7:

Surface area = 2 × (22/7) × 7 × (7 + 80)

$= 2 \times 22 \times 87$

$= 44 \times 87$

$= 3,828$ cm²

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(C) Cone with diameter = 14 cm, slant height = 10 cm

Total surface area = πr(r + l)

Radius (r) = 14 ÷ 2 = 7 cm

Slant height (l) = 10 cm

Using π = 22/7:

Surface area = (22/7) × 7 × (7 + 10)

$= 22 \times 17$

$= 374$ cm²

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(D) Sphere with radius = 10.5 cm

Surface area = 4πr²

Radius = 10.5 cm = 21/2 cm

r² = (10.5)² = 110.25

Using π = 22/7:

Surface area = 4 × (22/7) × 110.25

$= 4 \times \dfrac{22}{7} \times \dfrac{441}{4}$

$= 22 \times 63$

$= 1,386$ cm²

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Comparing surface areas:

(B) Cylinder: 3,828 cm²

(D) Sphere: 1,386 cm²

(C) Cone: 374 cm²

(A) Cube: 216 cm²

Decreasing order: (B), (D), (C), (A)