What is the volume of a pentagonal prism that has a base area of 5.16 cm2 and a height of 9 cm? 46.44 cm 3 19.32 cm 3 55.32 cm 3 14.16 cm 3
The Correct Answer and Explanation is:
The formula to calculate the volume of a prism is:V=Ab×hV = A_b \times hV=Ab×h
Where:
- VVV is the volume of the prism.
- AbA_bAb is the area of the base.
- hhh is the height of the prism.
Given:
- The area of the base (AbA_bAb) is 5.16 cm².
- The height (hhh) is 9 cm.
Substitute the values into the formula:V=5.16 cm2×9 cm=46.44 cm3V = 5.16 \, \text{cm}^2 \times 9 \, \text{cm} = 46.44 \, \text{cm}^3V=5.16cm2×9cm=46.44cm3
Thus, the volume of the pentagonal prism is 46.44 cm³.
Explanation:
The volume of a prism is simply the area of its base multiplied by its height. In this case, the base is a pentagon, but we don’t need the specific shape of the base to find the volume, as long as we know its area. The height is the perpendicular distance between the two bases (in this case, the top and bottom faces of the pentagonal prism). So, by multiplying the base area by the height, we get the volume of the prism.
Therefore, the correct answer is 46.44 cm³.
