A rectangular pyramid has

Question

a length of 7 cm and a
width of 9 cm. Its volume is
231 cubic centimeters. Use
the formula for the volume
of a pyramid to calculate
the height of this pyramid.
Show all your work.

Answer 1

To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:

$$V=\frac{1}{3}\times B\times h$$

where:

• $V$ is the volume,
• $B$ is the area of the base, and
• $h$ is the height of the pyramid.

Step 1: Calculate the area of the base

The base of the rectangular pyramid is a rectangle with length ($l$) and width ($w$). The area ($B$) can be calculated using the formula:

$$B=l\times w$$

Given:

• Length ($l$) = 7 cm
• Width ($w$) = 9 cm

Calculating $B$:

$$B=7,\text{cm}\times 9,\text{cm}=63,{\text{cm}}^2$$

Step 2: Plug the values into the volume formula and solve for height

We know the volume $V$ is 231 cubic centimeters. Now, we can use the volume formula:

$$231=\frac{1}{3}\times 63\times h$$

Step 3: Multiply both sides by 3 to eliminate the fraction

$$3\times 231=63\times h$$

Calculating the left side:

$$693=63\times h$$

Step 4: Solve for $h$

Now, we divide both sides by 63:

$$h=\frac{693}{63}$$

Calculating $h$:

$$h=11,\text{cm}$$

Conclusion

The height of the pyramid is $11,\text{cm}$.