Question

What is the surface area and volume of a composite figure made up of a hemisphere and a cone in terms of pi? The radius is 10, and the slant height is 15.

Ans: surface area: 350 pi units^2
volume: 1039.4 pi units^3

Answer 1

cone:
area = πrs
volume = 1/3 πr^2h = π/3 r^2√(s^2-r^2)

hemisphere:
area = 2πr^2
volume = 2/3 πr^3

So, plug in your numbers and you will get the desired answers. If not, come back with your work and we can see where you went wrong.

Answer 2

Cone surface area: π(10)(15)
= 150π
Hemisphere surface area: 2π(10)^2
= 200π

350π is the surface area

Cone volume: 1/3π(10)^2(11.2)
= 373.3π
I got the height by using the pythagorean theorem.

Hemisphere volume - 2/3π(10)^3
= 666.7π

= 1040π for the volume