Question

The surface area of a sphere is 2464 cm². If its radius be doubled then what will be the surface area of new sphere ?​​

Answer 1

Step-by-step explanation:

Given:-

• The surface area of a sphere = 2464cm²

To Find:-

• The surface area of new sphere if the radius is doubled.

Solution:-

Surface area of the sphere = 2464cm²

Let the radius of the sphere be r

Surface area of the sphere = 4πr²

$\sf \implies 4\pi r^2 = 2464$

$\sf \implies 4 \times \dfrac{22}{7} \times r^2 = 2464$

$\sf \implies \dfrac{88}{7} \times r^2 = 2464$

$\sf \implies r^2 = 2464 \times \dfrac{7}{88}$

$\sf \implies r^2 = 196$

$\sf \implies r = \sqrt{196}$

$\sf \implies r = 14$

$\sf If \: radius \: is\: doubled\:$

= 2r

= 2 × 14 = 28cm

$\sf Radius \: of \: new \: sphere \: (R)= 28cm$

$\sf Surface \: area \: of \: sphere = 4 \pi R^2$

$\sf = 4 \times \dfrac{22}{7} \times 28 \times 28$

$\sf = 4 \times 22 \times 4 \times 28$

$\sf = 9856$

$\underline{\boxed{\sf \therefore Surface \: area \: of \: new \: sphere = 9856cm^2}}$