Question

The area of a circle of radius 10 units is equal to the surface area of a sphere of radius 5 units.

a. true
b. false

Answer 1

True

Area of a circle = πr^2
So if r = 10: area = π*10^2
= 100π

Surface area of a sphere = 4πr^2
If r = 5: surface area = 4π*5^2
= 4π*25
= 100π

Answer 2

a.True

Explanation:

We are given that

Radius of circle=10 units

Radius of sphere=5 units

We have to find that the area of a circle of radius 10 units is equal to the surface area of a sphere of radius 5 units is true or not.

We know that

Area of circle=
`\pi r^2`

Substitute the value then we get

Area of circle=
`\pi (10)^2=100\pi` square units

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

Substitute the value of radius then we get

Area of sphere=
`4\pi* (5)^2=100\pi` square units

Area of circle=Area of sphere

Hence, the given statement is true.