Other 3-Dimensional Geometry - SAT Subject Test in Math I

Card 0 of 3

Question

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

Answer

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

Now substituting in our values we get:

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Question

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

Answer

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

$V= \frac{1}{2}(bh)h_2$

In our case our

Therefore,

$V=\frac{1}{2}(28)14$

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

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Question

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

Answer

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

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:

$area = 6\cdot side^2$

$\sqrt{6} = side$

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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