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:

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

The correct answer is Option (2) → (B), (D), (C), (A)

1. Calculations

• (A) Cube (Side $a = 6$ cm):

The total surface area of a cube is given by $6a^2$.

$\text{Area} = 6 \times (6^2) = 6 \times 36 = \mathbf{216 \text{ cm}^2}$

• (B) Cylinder (Diameter $d = 14$ cm, Height $h = 80$ cm):

Radius $r = \frac{14}{2} = 7$ cm.

Total Surface Area = $2\pi r(r + h)$

$\text{Area} = 2 \times \frac{22}{7} \times 7 \times (7 + 80)$

$\text{Area} = 44 \times 87 = \mathbf{3828 \text{ cm}^2}$

• (C) Cone (Diameter $d = 14$ cm, Slant height $l = 10$ cm):

Radius $r = \frac{14}{2} = 7$ cm.

Total Surface Area = $\pi r(r + l)$

$\text{Area} = \frac{22}{7} \times 7 \times (7 + 10)$

$\text{Area} = 22 \times 17 = \mathbf{374 \text{ cm}^2}$

• (D) Sphere (Radius $r = 10.5$ cm):

Total Surface Area = $4\pi r^2$

$\text{Area} = 4 \times \frac{22}{7} \times (10.5)^2$

$\text{Area} = 4 \times \frac{22}{7} \times 110.25$

$\text{Area} = 4 \times 22 \times 15.75 = \mathbf{1386 \text{ cm}^2}$

2. Comparison of Results