Question

The volume of the rectangular pyramid below is 1056 unitscubed
3
. Find the value of xx.
12 width
x length
22hieght
Answer
Attempt 1 out of 2

Answer 1

To find the value of \( x \) in the volume of the rectangular pyramid, we can use the volume formula for a pyramid:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

For a rectangular pyramid, the base area is given by the product of its length and width:

\[
\text{Base Area} = \text{length} \times \text{width} = x \times 12
\]

The height \( h \) is given as \( 22 \).

Now substituting these values into the volume formula:

\[
1056 = \frac{1}{3} \times (x \times 12) \times 22
\]

First, simplify the equation:

\[
1056 = \frac{1}{3} \times 12 \times 22 \times x
\]

Calculating \( 12 \times 22 \):

\[
12 \times 22 = 264
\]

Thus, the equation becomes:

\[
1056 = \frac{1}{3} \times 264 \times x
\]

Now, multiply both sides by 3 to eliminate the fraction:

\[
3 \times 1056 = 264 \times x
\]

Calculating \( 3 \times 1056 \):

\[
3 \times 1056 = 3168
\]

So the equation is now:

\[
3168 = 264 \times x
\]

Now, solve for \( x \) by dividing both sides by 264:

\[
x = \frac{3168}{264}
\]

Now, simplify \( \frac{3168}{264} \):

\[
x = 12
\]

Thus, the value of \( x \) is:

\[
\boxed{12}
\]