Question

The cone and the cylinder below have equal surface area. True or False?

Answer 1

1 Find the surface area of the cylinder

we know that

the surface area of a cylinder is equal to

`SA=2*area\ of\ the\ base +perimeter\ of\ the\ base*height`

`area\ of\ the\ base= \pi* r^(2)`

`perimeter\ of\ the\ base= 2*\pi* r`

`height=r`

Substitute

`SA=2*\pi*r^(2) +2*\pi*r*r`

`SA=4*\pi *r^(2)`

2 Find the surface area of the cone

we know that

the surface area of a cone is equal to

`SA=\pi*r^(2)+\pi *r*l`

`SA=\pi *r^(2)+\pi *r*2*r`

`SA=3* \pi *r^(2)`

3 Compare the surface area of the cylinder with the surface area of the cone

`4 \pi r^(2)\\eq 3 \pi r^(2)`

therefore

the answer is

False