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:
Answer & explanation
Correct answer: option 1
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
|
Shape |
Surface Area (cm²) |
|
(B) Cylinder |
3828 |
|
(D) Sphere |
1386 |
|
(C) Cone |
374 |
|
(A) Cube |
216 |