PSAT Math : Solid Geometry
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Example Question #311 : Geometry
A water tank takes the shape of a closed cylinder whose exterior has height 40 feet and a base with radius 12 feet; the tank is six inches thick throughout. To the nearest hundred, how many cubic feet of water does the tank hold?
Six inches is equal to 0.5 feet, so the height of the interior of the tank is
the radius of the base of the interior of the tank is
The amount of water the tank holds is the volume of the interior of the tank, which is
This rounds to 16,200.
Example Question #21 : How To Find The Volume Of A Cylinder
The above diagram is one of a cylindrical tub. The company wants to make a cylindrical tub with four times the volume, but whose base is only three times the radius. How high should this new tub be?
The volume of the given tub can be expressed using the following formula, setting 
The new tub should have four times this volume, or
The radius is to be three times that of the above tub, which will be
The height can therefore be calculated as follows:
Example Question #24 : How To Find The Volume Of A Cylinder
The above diagram is one of a cylindrical tub. The tub is holding water at 70% capacity. To the nearest cubic foot, how much more water can it hold?
The volume of the cylinder can be calculated using the following formula, setting 
The tub is 70% full, so it is 30% empty; it can hold
The problem asks for the number of cubic feet, so divide by the cube of 12, or 1,728:
The correct response is 14 cubic feet.
Example Question #25 : How To Find The Volume Of A Cylinder
Example Question #21 : How To Find The Volume Of A Cylinder
Two cylinders are full of milk. The first cylinder is 9” tall and has a base diameter of 3”. The second cylinder is 9” tall and has a base diameter of 4”. If you are going to pour both cylinders of milk into a single cylinder with a base diameter of 6”, how tall must that cylinder be for the milk to fill it to the top?
5"
12"
30"
9"
6.25"
6.25"
Volume of cylinder = π * (base radius)2 x height = π * (base diameter / 2 )2 x height
Volume Cylinder 1 = π * (3 / 2 )2 x 9 = π * (1.5 )2 x 9 = π * 20.25
Volume Cylinder 2 = π * (4 / 2 )2 x 9 = π * (2 )2 x 9 = π * 36
Total Volume = π * 20.25 + π * 36
Volume of Cylinder 3 = π * (6 / 2 )2 x H = π * (3 )2 x H = π * 9 x H
Set Total Volume equal to the Volume of Cylinder 3 and solve for H
π * 20.25 + π * 36 = π * 9 x H
20.25 + 36 = 9 x H
H = (20.25 + 36) / 9 = 6.25”
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