Checkpoint 3

Correct: A (116 cm$^2$)

Rectangle = $12 \times 8 = 96$ cm$^2$. Triangle = $\frac{1}{2} \times 8 \times 5 = 20$ cm$^2$. Total = $116$ cm$^2$.

Correct: B (142 cm$^2$)

$SA = 2(7 \times 5 + 7 \times 3 + 5 \times 3) = 2(35 + 21 + 15) = 2 \times 71 = 142$ cm$^2$.

Correct: B ($80\pi$ cm$^2$)

$CSA = 2\pi r h = 2\pi(4)(10) = 80\pi$ cm$^2$.

Correct: B ($36\pi$ cm$^3$)

$V = \frac{4}{3}\pi(3)^3 = \frac{4}{3}\pi(27) = 36\pi$ cm$^3$.

Correct: A ($96\pi$ cm$^3$)

$V = \frac{1}{3}\pi(6)^2(8) = \frac{1}{3}\pi(36)(8) = 96\pi$ cm$^3$.

Correct: B (1000 cm$^2$)

Closed = $2(20 \times 15 + 20 \times 10 + 15 \times 10) = 1300$ cm$^2$. Open top: subtract $20 \times 15 = 300$. Surface area = $1300 - 300 = 1000$ cm$^2$.

Correct: A ($3000\pi$ L)

$r = 1$ m. $V = \pi(1)^2(3) = 3\pi$ m$^3$ = $3000\pi$ L.

Correct: A ($125 - 5\pi$ cm$^3$)

Cube = $5^3 = 125$ cm$^3$. Cylinder = $\pi(1)^2(5) = 5\pi$ cm$^3$.

Correct: A (300 cm$^3$)

$A_{base} = \frac{1}{2} \times 5 \times 12 = 30$ cm$^2$. $V = 30 \times 10 = 300$ cm$^3$.

Correct: A ($\frac{3}{2}$)

Cylinder: $\pi r^2(2r) = 2\pi r^3$. Sphere: $\frac{4}{3}\pi r^3$. Ratio = $\frac{2\pi r^3}{\frac{4}{3}\pi r^3} = \frac{2}{\frac{4}{3}} = \frac{3}{2}$.