A rectangular pyramid has 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.

Question

40 words limit

Answer 1

The volume \( V \) of a pyramid is given by the formula:

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

For a rectangular pyramid:

\[ \text{Base Area} = \text{Length} \times \text{Width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]

Substituting into the volume formula:

\[ 231 = \frac{1}{3} \times 63 \times h \]

Multiplying both sides by 3:

\[ 693 = 63h \]

Solving for \( h \):

\[ h = \frac{693}{63} = 11 , \text{cm} \]

Thus, the height of the pyramid is 11 cm.

Answer 2

Where did 231 and 693 come from?

Answer 3

Apologies for any confusion. Here’s a clearer breakdown:

1. Given Information:

   • Length of the pyramid, \( l = 7 , \text{cm} \)
   • Width of the pyramid, \( w = 9 , \text{cm} \)
   • Volume of the pyramid, \( V = 231 , \text{cm}^3 \)

2. Base Area Calculation: \[ \text{Base Area} = l \times w = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]

3. Volume Formula: The volume \( V \) of a pyramid is calculated using: \[ V = \frac{1}{3} \times \text{Base Area} \times h \]

4. Substituting in Values: \[ 231 = \frac{1}{3} \times 63 \times h \]

5. Multiplying Both Sides by 3: This step eliminates the fraction: \[ 3 \times 231 = 63h \implies 693 = 63h \]

6. Solving for Height \( h \): To find \( h \): \[ h = \frac{693}{63} = 11 , \text{cm} \]

Thus, the height of the pyramid is ( 11 , \text{cm}.