Question

the formula for the volume of a pyramid is $v = \frac{1}{3}bh$, where $b$ is the area of the base of the pyramid and $h$ is the height of the pyramid. the figure below is made of two identical rectangular pyramids. what is the volume of the entire figure? image of two pyramids with 8 in, 6 in, 10 in (twice) options: 960 cubic inches, 160 cubic inches, 480 cubic inches, 320 cubic inches

Explanation:

Step1: Find the area of the base (B)

The base is a rectangle with length 8 in and width 6 in. The area of a rectangle is \( B = length \times width \), so \( B = 8 \times 6 = 48 \) square inches.

Step2: Find the volume of one pyramid

The height (h) of one pyramid is 10 in. Using the volume formula for a pyramid \( V = \frac{1}{3}Bh \), substitute \( B = 48 \) and \( h = 10 \): \( V_{one} = \frac{1}{3} \times 48 \times 10 = 160 \) cubic inches.

Step3: Find the volume of the entire figure (two pyramids)

Since there are two identical pyramids, the total volume is \( V_{total} = 2 \times V_{one} = 2 \times 160 = 320 \) cubic inches. Wait, no, wait. Wait, let's recalculate. Wait, \( \frac{1}{3} \times 48 \times 10 = 160 \), then two pyramids: \( 2 \times 160 = 320 \)? Wait, no, wait the height of each pyramid is 10? Wait the figure has two pyramids, each with height 10? Wait the base is 8x6, so B=48. Then one pyramid: \( \frac{1}{3} \times 48 \times 10 = 160 \). Two pyramids: 1602=320? But wait, let me check again. Wait, maybe I made a mistake. Wait, 4810=480, divided by 3 is 160. Then two pyramids: 160*2=320. Wait, but the options have 320. Wait, but let me check the steps again.

Wait, Step1: Base area B = 86=48. Correct. Step2: Volume of one pyramid: (1/3)4810. 4810=480, 480/3=160. Correct. Step3: Two pyramids: 160*2=320. So the total volume is 320 cubic inches.

Answer:

320 cubic inches