SAT Mathematics Practice Test 3

Question : 45 of 58

Marks: +1, -0

A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet?

261.8
785.4
916.3
1,047.2

Validate

Solution:

Choice

D

is correct.
The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed.
The silo is made up of a cylinder with height 10 feet

( {ft})

and base radius 5 feet and two cones, each having height

5 {ft}

and base radius

5 {ft}

.
The formulas

V_{\;\text "cylinder "\;}=π r^{2} h

and

V_{\;\text "cone "\;}=\;{1}/{3} π r^{2} h

can be used to determine the total volume of the silo.
since the two cones have identical dimensions,
the total volume, in cubic feet, of the silo is given by

V_{\;\text "silo "\;}=π(5)^{2}(10)+(2)(\;{1}/{3}) π(5)^{2}(5)=(\;{4}/{3})(250) π,

which is approximately equal to 1,047.2 cubic feet.
Choice

{A}

is incorrect because this is the volume of only the two cones.
Choice

{B}

is incorrect because this is the volume of only the cylinder.
Choice C is incorrect because this is the volume of only one of the cones plus the cylinder.

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