Solve the problem.
-A heat duct in the college library has a circular cross section with a radius of 10 inches and a length of 29 feet. How much paint (in square feet)is needed to paint the duct?
A) $75.9 \mathrm { ft } ^ { 2 }$
B) $910.6 \mathrm { ft } ^ { 2 }$
C) $151.8 \mathrm { ft } ^ { 2 }$
D) $1821.2 \mathrm { ft } ^ { 2 }$

Question

Solve the problem.
-A heat duct in the college library has a circular cross section with a radius of 10 inches and a length of 29 feet. How much paint (in square feet)is needed to paint the duct? 
A) $75.9 \mathrm { ft } ^ { 2 }$
B) $910.6 \mathrm { ft } ^ { 2 }$
C) $151.8 \mathrm { ft } ^ { 2 }$
D) $1821.2 \mathrm { ft } ^ { 2 }$

Quizplus · Accepted Answer

To find the surface area of the duct (which is a cylinder), use the formula $2\pi rh$, where $r$ is the radius and $h$ is the height (or length, in this case). Convert the length from feet to inches (1 foot = 12 inches) to match the radius' unit, so $29 \text{ feet} = 29 \times 12 = 348 \text{ inches}$. Then, $2 \times \pi \times 10 \times 348 = 2\pi \times 10 \times 348 \approx 21912 \text{ square inches}$. Convert square inches to square feet ($1 \text{ square foot} = 144 \text{ square inches}$), so $21912 \div 144 \approx 152.0 \text{ square feet}$, which rounds to $151.8 \text{ square feet}$.

Solve the Problem 75.9ft275.9 \mathrm { ft } ^ { 2 }75.9ft2

Solve the Problem $75.9 \mathrm { ft } ^ { 2 }$