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Area, perimeter, volume, and surface area — SHSAT practice questions

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Practice 141 Area, perimeter, volume, and surface area questions in the app

What this topic is

Area, perimeter, volume, and surface area on the SHSAT Mathematics section covers two- and three-dimensional measurement: finding a missing length from a given area or perimeter, converting among related formulas, and counting unit cubes inside a solid.

Sample questions

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Question 1Mid

The side lengths of a rectangle are in the ratio $5:8$. If the perimeter of the rectangle is 78, what is the area of the rectangle?

A117✗ Not this oneB195✗ Not this oneC312✗ Not this oneD360✓ Correct

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Answer: D — 360

The perimeter is $2(5k+8k)=26k$. Since $26k=78$, $k=3$. The side lengths are 15 and 24, so the area is $15\cdot24=360$.

Question 2Mid

A rectangular prism is built from unit cubes and has dimensions 4 units by 5 units by 6 units. How many of the unit cubes do not touch any outside face of the prism?

A12✗ Not this oneB18✗ Not this oneC24✓ CorrectD36✗ Not this one

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Answer: C — 24

Removing the outside layer from each dimension leaves an interior block measuring $(4-2)$ by $(5-2)$ by $(6-2)$ unit cubes. That is $2\cdot3\cdot4=24$ cubes that do not touch any outside face.

Question 3Mid

A circular window has an area of $121\pi$ square inches. What is the circumference of the window in inches?

A$11\pi$✗ Not this oneB$22\pi$✓ CorrectC$121\pi$✗ Not this oneD$242\pi$✗ Not this one

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Answer: B — $22\pi$

From $\pi r^2=121\pi$, the radius is 11 inches. Therefore, the circumference is $2\pi(11)=22\pi$ inches.

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