Question

Here are two spheres, with
radii 3 cm and 4.5 cm
respectively. The surface
area of the smaller sphere is
367 cm. What is the surface
area of the larger sphere?
4.6 cm
3 cm
A) 417 cm2
C) 817 cm2
B) 547 cm2
D) 121.57 cm2

Answer 1

Given:

Radii of two spheres are 3 cm and 4.5 cm  respectively.

Surface  area of the smaller sphere is  367 cm.

To find:

The surface area of the larger sphere.

Solution:

We know that, area of similar spheres is proportional to the square of there radii.

$\dfrac{A_1}{A_2}=\dfrac{(r_1)^2}{(r_2)^2}$

On substituting the values, we get

$\dfrac{367}{A_2}=\dfrac{(3)^2}{(4.5)^2}$

$\dfrac{367}{A_2}=\dfrac{9}{20.25}$

On cross multiplication, we get

$(367)(20.25)=9A_2$

$7431.75=9A_2$

Divide both sides by 9.

$\dfrac{7431.75}{9}=A_2$

$825.75 =A_2$

Therefore, the area of larger sphere is 825.75 cm².

Note: All options are incorrect.