Difference between revisions of "2012 CEMC Gauss (Grade 7) Problems/Problem 21"
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==Problem== | ==Problem== | ||
| − | A triangular prism has a volume of <math>120 cm^{3}. Two edges of the triangular prism measure 3 cm and 4 cm, as shown. | + | A triangular prism has a volume of <math>120 cm^{3}</math>. Two edges of the triangular prism measure 3 cm and 4 cm, as shown. |
{{Template:Image needed}} | {{Template:Image needed}} | ||
The height of the prism, in cm, is | The height of the prism, in cm, is | ||
| − | < | + | |
| + | <math>\text{(A)}\ 12 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 8 </math> | ||
==Solution== | ==Solution== | ||
The volume of the triangular prism will be the area of the base multiplied by its height. | The volume of the triangular prism will be the area of the base multiplied by its height. | ||
| − | Let < | + | Let <math>A</math> and <math>h</math> be the area of the base and the height, respectively. We then have: |
| − | < | + | <math>A = \frac{3 cm * 4 cm}{2} = 6 cm^2</math> |
| − | < | + | <math>A * h = V</math> |
| − | < | + | <math>6 cm^2 * h = 120 cm^3</math> |
| − | < | + | <math>h = \frac{120 cm^3}{6 cm^2} = 20 cm</math> |
| − | Thus, the answer is < | + | Thus, the answer is <math>\boxed {\textbf {(B) } 20}</math>. |
Latest revision as of 19:39, 1 May 2025
Problem
A triangular prism has a volume of 
. Two edges of the triangular prism measure 3 cm and 4 cm, as shown.
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
The height of the prism, in cm, is
Solution
The volume of the triangular prism will be the area of the base multiplied by its height.
Let 
and 
be the area of the base and the height, respectively. We then have:
Thus, the answer is 
.
