Surface Area & Volume — Cylinder, Cone & Sphere

Cylinder

Meaning: A cylinder has two equal circular bases.

Definition: Cylinder volum$e = p$i $r^{2}$ h and curved surface are$a = 2$ $\pi$ r h.

A pipe or tin can is often modelled as a cylinder.

Cone

Meaning: A cone has a circular base and one vertex.

Definition: Cone volum$e = 1 / 3$ $\pi$ $r^{2}$ h and curved surface are$a = p$i r l.

The slant height l is the length along the curved side.

Sphere

Meaning: A sphere is a round solid.

Definition: Sphere volum$e = 4 / 3$ $\pi$ $r^{3}$ and surface are$a = 4$ $\pi$ $r^{2}$.

A ball is close to a sphere.

Hemisphere

Meaning: A hemisphere is half a sphere.

Definition: Curved surface area of hemispher$e = 2$ $\pi$ $r^{2}$ and total surface are$a = 3$ $\pi$ $r^{2}$.

A bowl can be modelled as a hemisphere.

Easy

Question: Find the volume of a cylinder with $r = 7$ cm and $h = 10$ cm. Use $\pi$ = 22 / 7.

1. $V = p$i $r^{2}$ h.
2. $V = 22 / 7$ x 7 x 7 x 10.
3. $V = 1540$ c$m^{3}$.

Medium

Question: Find the CSA of a cone with $r = 5$ cm and $l = 12$ cm. Use $\pi$ = 3.14.

1. CS$A = p$i r l.
2. CS$A = 3$.14 x 5 x 12.
3. CS$A = 188$.4 c$m^{2}$.

Exam-level

Question: Find the surface area of a sphere of radius 3 cm. Use $\pi$ = 3.14.

1. S$A = 4$ $\pi$ $r^{2}$.
2. S$A = 4$ x 3.14 x 3 x 3.
3. S$A = 113$.04 c$m^{2}$.