Question

A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Tran computes the amount of paint needed to cover the sphere. Which statement about the amount of paint found by Tran is true?

Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere
Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.
Tran found the minimum amount of paint needed to cover both hemispheres.
Tran found the minimum amount of paint needed to cover the bases of both hemispheres.

Answer 1

The statement about the amount of paint found by Tran is true is:

Tran found the minimum amount of paint needed to cover both hemispheres.

Explanation:

As we know that the amount of paint that will be required to paint the sphere is equal to the curved surface area of the sphere also as the sphere is cut into two equal hemispheres hence the paint required to paint the sphere is equal to the curved surface area of two hemispheres.

As the sphere is to be painted from outside this means that both the hemispheres are painted from outside.

Hence, the amount of paint required is equal to : 4πr²

( Since the curved area of sphere is: 4πr² )

• Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere

This option is incorrect.

Since, the curved surface area of a hemisphere=2πr²≠4πr²

• Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.

This option is incorrect.

Since the total surface area of one hemisphere= 3πr²≠4πr²

• Tran found the minimum amount of paint needed to cover both hemispheres.

This is the correct option.

Since, The amount of paint required to paint both the hemisphere is:

2πr²+2πr²=4πr²

• Tran found the minimum amount of paint needed to cover the bases of both hemispheres.

This option is incorrect.

Since in order to cover the vase of both hemispheres the amount of paint required is:

πr²+πr²=2πr²≠4πr²

( Since the surface area of base is: πr² )

Hence, the correct answer is

Tran found the minimum amount of paint needed to cover both hemispheres.

Answer 2

we know that

the sphere is divided into two hemispheres
the two hemispheres are equals

if Tran computes the amount of paint needed to cover the sphere
therefore
Tran computes the amount of paint needed to cover both hemispheres.

the answer is
Tran found the minimum amount of paint needed to cover both hemispheres.

[surface area of sphere]=4*pi*r²
[surface area of each hemisphere]=2*pi*r²

circumference=18.84 cm------> 2*pi*r------> r=18.84/(2*pi)------> 3cm
[surface area of each hemisphere]=2*pi*3²---------> 56.52 cm²

surface area of sphere=2*56.52=113.04 cm²