Question

QIB Solve.
2
(1) The radius of a sphere is R. Find the ratio of its surface area to
the area of a circle of the same radius.​

Answer 1

Answer:

• The ratio of the surface area of the sphere to area of the circle is 4 : 1.

Step-by-step explanation:

Given that:

• The radius of a sphere is R.
• The radius of a circle is R.

To Find:

• The ratio of the surface area of the sphere to the area of the circle.

Solution:

As we know that,

• Surface Area of a sphere = 4πr²
• Area of a circle = πr²

Where,

• r = Radius

Finding surface area of a sphere with radius as R:

Surface Area of the sphere = 4πR²

Finding area of a circle with radius as R:

Area of the circle = πR²

Finding ratio between surface area of the sphere and area of the circle:

$\sf{\longrightarrow4\pi R^2:\pi R^2}$

Writing in the form of ratio:

$\sf{\longrightarrow\dfrac{4\pi R^2}{\pi R^2}}$

$\sf{\longrightarrow\dfrac{4\pi\times R\times R}{\pi\times R\times R}}$

Cutting similar terms:

$\sf{\longrightarrow\dfrac{4\!\!\not{\pi}\times \!\!\!\not{R}\times \!\!\!\not{R}}{\!\!\!\not{\pi}\times \!\!\!\not{R}\times \!\!\!\not{R}}}$

$\sf{\longrightarrow\dfrac{4}{1}}$

Writing in ratio:

$\bf{\longrightarrow4:1}$

Hence,

• The ratio is 4 : 1.