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SAT II Math I : Other 3-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #52 : 3 Dimensional Geometry

A rectangular prism has a height of 4 in., length of 8in., and a width of 7in. Find the volume of the prism.

Possible Answers:

$146\ \textup{in.}$

$17\ \textup{in.}$

$230\ \textup{in.}$

$224\ \textup{in.}$

Correct answer:

$224\ \textup{in.}$

Explanation:

To find the volume of a rectangular prism we use the equation of:

V=l*w*h

Now substituting in our values we get:

V=8*7*4

V=56*4

V=224

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Example Question #2 : Other 3 Dimensional Geometry

What is the volume of a triangular prism having a base of 2, a height of 8, and second height of 14?

Possible Answers:

112

102

Correct answer:

112

Explanation:

To find the volume of a triangular prism we use the equation

$V= \frac{1}{2}(b*h)*h_2$

In our case our b=2, h=8, h_2=14

Therefore,

$V=\frac{1}{2}(2*8)*14$

$V=\frac{1}{2}(16)*14$

V=8*14

V=112

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Example Question #2 : Other 3 Dimensional Geometry

If a cube has a surface area of then what is the the length of its longest diagonal?

Possible Answers:

$\sqrt{6}$

$3\sqrt{2}$

216

$\frac{1}{3}\sqrt{3}$

Correct answer:

$3\sqrt{2}$

Explanation:

The longest diagonal of a cube transverses the interior of the figure:

Cube diagonal

This distance is defined by the super pythagorean theorem :

$distance = \sqrt{a^2+b^2+c^2}$

where , , and are the length, width, and height. Because the figure is a cube, all three are the same measure, and each is the side of the cube.

We can use the given surface area to find the length of the side:

$area = 6\cdot side^2$

36 = 6 side^2

6 = side^2

$\sqrt{6} = side$

We can use this value for the side to plug into the super pythagorean theorem

$distance = \sqrt{a^2+b^2+c^2}$

$distance = \sqrt{\sqrt{6}^2+\sqrt{6}^2+\sqrt{6}^2}$

$distance = \sqrt{18}$

Which can be simplified to

$3\sqrt{2}$

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All SAT II Math I Resources

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SAT II Math I : Other 3-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #52 : 3 Dimensional Geometry

Example Question #2 : Other 3 Dimensional Geometry

Example Question #2 : Other 3 Dimensional Geometry

All SAT II Math I Resources

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