Question

1. If the diameter of a sphere is d and curved surface
area S, then show that S = πd square Hence find the
surface area of a sphere whose diameter is 4.2 cm.​

Answer 1

S = $\pi d^{2}$ , proved.

The area of curved surface area = 55.44 $cm^{2}$

Step-by-step explanation:

Given,

The diameter of a sphere =d and

The curved surface  area of a sphere= S

To prove that, S = $\pi d^{2}$ .

To find, the  surface area of a sphere whose diameter(4.2 cm)=

∴ The radius of a sphere = $\dfrac{d}{2}$

We know that,

The curved surface  area of a sphere, S =$4\pi r^{2}$

⇒ S = $4\pi (\dfrac{d}{2})^{2}$

⇒ S = $4\pi \dfrac{d^2}{4}$

∴ S = $\pi d^{2}$ , proved.

The  surface area of a sphere whose diameter is 4.2 cm

= $\dfrac{22}{7}\times (4.2)^{2}$

= $\dfrac{22}{7}\times 4.2\times 4.2$

= $22\times 0.6\times 4.2$

= 13.2 × 4.2 $cm^{2}$

= 55.44 $cm^{2}$

Thus, the area of curved surface area = 55.44 $cm^{2}$

Answer 2

Step-by-step explanation:

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