A thin wire is bent into the shape of a semicircle $x ^ { 2 } + y ^ { 2 } = 4 , x 0$ If the linear density is $4$ , find the exact mass of the wire.
A) $3 \pi$
B) $18 \pi$
C) $8 \pi$
D) $8 \pi ^ { 2 }$
E) $2 \pi$

Question

A thin wire is bent into the shape of a semicircle $x ^ { 2 } + y ^ { 2 } = 4 , x > 0$ If the linear density is $4$ , find the exact mass of the wire.
A) $3 \pi$
B) $18 \pi$
C) $8 \pi$
D) $8 \pi ^ { 2 }$
E) $2 \pi$

Quizplus · Accepted Answer

The semicircle has a radius of 2. The length of the semicircle is $\pi \times 2 = 2\pi$. With a linear density of 4, the mass is $4 \times 2\pi = 8\pi$.

A Thin Wire Is Bent into the Shape of a Semicircle