To determine the factor by which the volume of a right square pyramid is multiplied when its height is increased by a factor of 8, while keeping the dimensions of its base unchanged, we need to understand the volume formula for a pyramid.
The volume \( V \) of a right square pyramid is given by:
\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\]
Let's denote:
- \( A \) as the area of the base,
- \( h \) as the original height,
- and \( h' = 8h \) as the new height (since the height is multiplied by 8).
The original volume \( V \) of the pyramid is:
\[
V = \frac{1}{3} A h
\]
When the height is multiplied by 8, the new volume \( V' \) becomes:
\[
V' = \frac{1}{3} A \times (8h)
\]
Simplifying it:
\[
V' = \frac{1}{3} A \times 8h = 8 \left( \frac{1}{3} A h \right) = 8V
\]
Thus, the volume of the pyramid is multiplied by a factor of 8 when the height is multiplied by 8, with the base dimensions remaining the same.
The correct answer is:
\[ D. 8 \]
By what factor is the volume of a right square pyramid multiplied if its height is multiplied by 8 but the dimensions of its base are unchanged?
A. 1/16
B. 1/8
C. 4
D. 8
1 answer