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A shed is shaped like a cuboid surmounted by a half cylinder, as shown in the figure. The base of the cuboid is $7\,\mathrm{m}\times 15\,\mathrm{m}$ and its height is $8\,\mathrm{m}$. What is the volume of air the empty shed can hold? Take $\pi=\frac{22}{7}$. 
A$840\,\mathrm{m}^3$
B$1128.75\,\mathrm{m}^3$
C$1287.5\,\mathrm{m}^3$
D$827.15\,\mathrm{m}^3$
Answer & Solution
Correct answer: B. $1128.75\,\mathrm{m}^3$
The shed's volume is the sum of the cuboid and the half-cylinder. Cuboid volume $=15\times7\times8=840\,\mathrm{m}^3$. The half-cylinder has radius $3.5\,\mathrm{m}$ and length $15\,\mathrm{m}$, so its volume is $\frac12\pi r^2h=\frac12\times\frac{22}{7}\times3.5^2\times15=288.75\,\mathrm{m}^3$. Total volume $=840+288.75=1128.75\,\mathrm{m}^3$.
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