Find the volume of a pyramid with height and base an equilateral triangle with side a = .

Question

Find the volume of a pyramid with height  and base an equilateral triangle with side a =  .

Quizplus · Accepted Answer

The formula for the volume of a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height.

To find the area of the equilateral triangle base, we can use the formula $A=\frac{\sqrt{3}}{4}s^2$, where $s$ is the length of a side. Substituting $s=11eaa3e5_5587_9b7d_9f8f_67a97a57d56c_TB5971_00$ gives us $A=\frac{\sqrt{3}}{4}(11eaa3e5_5587_9b7d_9f8f_67a97a57d56c_TB5971_00)^2=11eaa3e5_5587_e9a2_9f8f_4f3eb2500fb8_TB5971_11$.

Therefore, the volume of the pyramid is $V=\frac{1}{3}(11eaa3e5_5587_e9a2_9f8f_4f3eb2500fb8_TB5971_11)(11eaa3e5_5587_9b7c_9f8f_c163407c1c76_TB5971_11)=11eaa3e5_5587_e9a3_9f8f_551a79f3cffc_TB5971_11$.

The only choice that matches this answer is E.

Find the Volume of a Pyramid with Height and Base