Question

True or False The area of a circle of radius 14 units is equal to the surface area of a sphere radius 7 units

Answer 1

The answer is true. The area of a circle of radius 14 units is equal to the surface area of a sphere radius 7 units

Answer 2

True

Explanation:

Given: Statement :"The area of a circle of radius 14 units is equal to the surface area of a sphere radius 7 units"

We have to choose whether the given statement s true or false.

Consider the given statement.

The area of a circle of radius 14 units is equal to the surface area of a sphere radius 7 units

We first find the area of circle with 14 units radius and area of a sphere with 7 units radius and compare the two values.

We know,

Area of circle =
`\pi r^2`

given : r = 14 units

So, Area of circle =
`\pi (14)^2`

Simplify, we have,

Area of circle =
`196\pi` units²

Now,

Area of sphere =
`4\pi r^2`

given : r = 7 units

So, Area of sphere =
`4\pi (7)^2`

Simplify, we have,

Area of sphere =
`196\pi` units²

Since, Area of circle with radius 14 units is equal to the area of sphere with radius 7 units.

Thus, The given statement is true.