Source: GMAT Paper Tests
The figure above shows the shape and dimensions of the inside of a container that has a flat rectangular top and semicircular ends perpendicular to the top. When the container is loaded to its exact capacity with slag that weighs 50 pounds per cubic foot, what will be the approximate weight, in tons, of the slag in the container?
(1 ton = 2000 pounds)
A. 2
B. 4
C. 6
D. 8
E. 10
The OA is C.
The figure above shows the shape and dimensions of the
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The container show is half of a cylinder
height (h) = 10 ft
radius of base (r) = $$\frac{8}{2}=4\ ft$$
$$Volume=\frac{1}{2}\pi r^2h$$
$$=\frac{1}{2}\cdot\frac{22}{7}\cdot4^2\cdot10$$
$$=\frac{1}{2}\cdot\frac{22}{7}\cdot16\cdot10$$
$$=251.43$$
Weight of slag $$=251.43\ \cdot50$$
$$=12591.5$$
$$\sin ce\ 1\ ton=2000$$
$$weight\ in\ tons=\frac{12571.5}{2000}$$
$$=6.28575=6$$
$$answer\ is\ Option\ C$$
height (h) = 10 ft
radius of base (r) = $$\frac{8}{2}=4\ ft$$
$$Volume=\frac{1}{2}\pi r^2h$$
$$=\frac{1}{2}\cdot\frac{22}{7}\cdot4^2\cdot10$$
$$=\frac{1}{2}\cdot\frac{22}{7}\cdot16\cdot10$$
$$=251.43$$
Weight of slag $$=251.43\ \cdot50$$
$$=12591.5$$
$$\sin ce\ 1\ ton=2000$$
$$weight\ in\ tons=\frac{12571.5}{2000}$$
$$=6.28575=6$$
$$answer\ is\ Option\ C$$