Question

The volume of a prism is found by multiplying the area of the base by the height. A rectangular prism has a volume of 144 cm^3, and a square base with a width of 3 cm. What is the height of the prism, in cm?
a. 4
b. 8
c. 48
d. 16

Answer 1

If the prism's base is a square, and its width is 3 cm long that means its (the base's) length is also 3 cm. Since it is a square and a square's all sides has the same length. So let's find the base's area. To find it we'll multiply the length of its two sides. Since all sides has the same length, which is 3 cm. 3 times 3 gives us the area of the base.

$3\cdot 3=\quad 9\\ \\ \boxed { 9\quad { cm }^{ 2 } }$

To find the prism's volume, we multiply its base area with its height. Let's call the height with the variable 'h' . h times base area (which is 9) will give us the volume of the prism (which is 144).

Let's build the equation.

$h\cdot 9=144$

To solve for h, let's divide both sides by 9.

$h\cdot 9=144\\ \\ \frac { h\cdot 9 }{ 9 } =\frac { 144 }{ 9 } \\ \\ h\cdot \frac { 9 }{ 9 } =\frac { 16\cdot 9 }{ 9 } \\ \\ h\cdot 1=16\cdot \frac { 9 }{ 9 } \\ \\ h=16\cdot 1\\ \\ h=16$

So we've found h (height) as 16 cm.

$height=\quad \boxed { 16\quad cm }$

The answer is : d. 16