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Surface Area

This worksheet covers Surface Area, which is part of the Area, Surface Area, Volume and Density module in the SAT Math course. Practice problems are designed to strengthen key concepts and build confidence.

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Surface Area

Area, Surface Area, Volume and Density • SAT Math

Set 4 — Mastery

A cylinder has a radius of $r$ and a height of $h$ . What is the formula for the surface area $S$ of the cylinder? $S = ?$

$2\pi r(h + r)$

$rac{1}{3} \pi r^{2} h$

$2\pi rh$

$rac{2}{3} \pi r^{3} + rac{1}{3} \pi r^{2} h$

A cube has a side length of $s$ . What is the surface area of the cube?

$6s^{2}$

$12s^{2}$

$s^{3}$

$4s^{2}$

What is the surface area of a sphere with a radius of $r$ ?

$4\pi r^{2}$

$2\pi r^{2}$

$\frac{4}{3}\pi r^{3}$

$3\pi r^{2}$

A rectangular prism has dimensions $l$ , $w$ , and $h$ . What is the formula for the surface area $S$ of the rectangular prism?

$2(lw + lh + wh)$

$lwh$

$2(l + w + h)$

$l + w + h$

If a cone has a radius of $r$ and a height of $h$ , what is the formula for its lateral surface area?

$\pi r \sqrt{r^{2} + h^{2}}$

$\pi r^{2} h$

$\frac{1}{3} \pi r^{2} h$

$\pi r^{2} + \pi r \sqrt{r^{2} + h^{2}}$

A prism has a height of $h$ and a base that is a triangle with area $A$ . What is the formula for the surface area $S$ of the prism?

$S = 2A + Ph$

$S = A + Ph$

$S = Ah$

$S = 3A$

A cylinder's radius is doubled while its height remains the same. How does the surface area change?

Increases by a factor of 4

Increases by a factor of 2

Stays the same

Increases by a factor of 8

If the surface area of a sphere is $100\pi$ , what is the radius of the sphere?

The surface area of a rectangular prism is $150$ square units. If the length is $5$ units and the height is $10$ units, what is the width?

10.

A cone has a radius of $r$ and a slant height of $l$ . What is the formula for its total surface area?

$\pi r^{2} + \pi rl$

$\pi rl$

$\pi r^{2} + r^{2}$

$\frac{1}{3} \pi r^{2} l$

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Other Sets

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Set 1Foundation Set 2Foundation Set 3Foundation Set 4Mastery Set 5Mastery Custom Worksheet