Perimeter and arc length Practice Questions (Grade 10)

Perimeter and arc length. Game on.

Perimeter and arc length is a grade 10 math skill aligned to Common Core standard HSG.C.B.5: derive the fact that the length of the arc intercepted by an angle is proportional to the radius, and derive the formula for the area of a sector. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 perimeter and arc length problems our math games drill.

CCSS HSG.C.B.515 questions in the bank

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Warm-upeasy

Find the arc length of a $90°$ arc on a circle with radius $4$ . Use $\pi = 3$ .

$L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 4 = 6$ .

Mid-gameeasy

A triangle has sides $7$ , $10$ , and $12$ . What is its perimeter?

$P = 7 + 10 + 12 = 29$ .

Mid-gameeasy

Find the arc length of a $180°$ arc on a circle with radius $5$ . Use $\pi = 3$ .

$L = \dfrac{180}{360} \times 2 \pi r = \dfrac{1}{2} \times 2 \times 3 \times 5 = 15$ .

Mid-gameeasy

A rectangular garden measures $15$ by $6$ . How many units of fencing are needed to go all the way around it?

$P = 2(15 + 6) = 2 \cdot 21 = 42$ .

Mid-gameeasy

Find the arc length of a $90°$ arc on a circle with radius $6$ . Use $\pi = 3$ .

$L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 6 = 9$ .

Mid-gameeasy

Find the arc length of a $180°$ arc on a circle with radius $3$ . Use $\pi = 3$ .

$L = \dfrac{180}{360} \times 2 \pi r = \dfrac{1}{2} \times 2 \times 3 \times 3 = 9$ .

Mid-gameeasy

Find the arc length of a $90°$ arc on a circle with radius $2$ . Use $\pi = 3$ .

$L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 2 = 3$ .

Buzzer beatereasy

A semicircle has radius $10$ . Its curved edge has length $k\pi$ . What is the value of $k$ ?

Half the circumference is $\dfrac{1}{2} \cdot 2 \pi \cdot 10 = 10\pi$ , so $k = 10$ .

Perimeter and arc length. Game on.

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