What is the volume of the rectangular pyramid

Question

the height (or slant length idrk) is 10 on the left and 11.66 on the right
the base on the left is 12 and the right is also 12

Answer 1

To find the volume of a rectangular pyramid, you can use the formula: V = (1/3) * base area * height.

First, we need to find the base area. Since the base is a rectangle, the base area can be calculated as base length * base width. In this case, the base length is 12 and the base width is 12, so the base area is 12 * 12 = 144 square units.

Next, we need to find the height of the pyramid. The height of the pyramid is the vertical distance from the apex to the base. It is given as 10 on the left side and 11.66 on the right side. Since the height of the pyramid is calculated along the slant, we need to calculate the slant height of the pyramid. Using the Pythagorean theorem, we can calculate the slant height:

slant height = √(height^2 + ((base width/2)^2))
= √(10^2 + (6^2))
= √(100 + 36)
= √136
≈ 11.66

Now we have all the necessary information to calculate the volume of the rectangular pyramid:

V = (1/3) * base area * height
V = (1/3) * 144 * 11.66
V ≈ 580.8 cubic units

Therefore, the volume of the rectangular pyramid is approximately 580.8 cubic units.

Answer 2

I thought it was 559.68

Answer 3

Let's recalculate the volume to confirm the correct answer.

The base area is still 144 square units, and the slant height of the pyramid is 11.66 units.

Using the formula V = (1/3) * base area * height:

V = (1/3) * 144 * 11.66
V = (1/3) * 1670.24
V = 559.68 cubic units

Therefore, the correct volume of the rectangular pyramid is indeed 559.68 cubic units. Thank you for pointing that out.

Answer 4

Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.(1 point)

Answer 5

To find the volume of the rectangular pyramid-shaped tent, we can use the formula:

V = (1/3) * base area * height

Given:
Height (h) = 75 inches
Base width (w) = 111 inches
Base length (l) = 111 inches

First, let's find the base area of the pyramid:

Base area = base width * base length
Base area = 111 * 111
Base area = 12321 square inches

Now we can calculate the volume of the rectangular pyramid-shaped tent:

V = (1/3) * 12321 * 75
V = (1/3) * 924075
V = 308025 cubic inches

Therefore, the volume of the pyramid-shaped tent is 308025 cubic inches.

Answer 6

A cell phone telecommunication tower stands in the shape of a rectangular pyramid. The tower stands 80 m tall and rests on a base that is 15 m by 20 m. What is the volume of the tower?

Answer 7

To find the volume of the rectangular pyramid-shaped tower, we can use the formula:

V = (1/3) * base area * height

Given:
Height (h) = 80 m
Base width (w) = 15 m
Base length (l) = 20 m

First, let's find the base area of the pyramid:

Base area = base width * base length
Base area = 15 * 20
Base area = 300 square meters

Now we can calculate the volume of the rectangular pyramid-shaped tower:

V = (1/3) * 300 * 80
V = (1/3) * 24000
V = 8000 cubic meters

Therefore, the volume of the pyramid-shaped tower is 8000 cubic meters.

Answer 8

A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 x 2.75 x 2.75 in. What is the approximate volume of the ornament? Round your answer to the nearest hundredth.

Answer 9

To find the volume of the square pyramid-shaped holiday ornament, we can use the formula:

V = (1/3) * base area * height

Given:
Base side length (s) = 2.75 in
Height (h) = 2.75 in (since it is a square pyramid)

First, let's find the base area of the pyramid:

Base area = base side length^2
Base area = 2.75^2
Base area = 7.5625 square inches

Now we can calculate the volume of the square pyramid-shaped ornament:

V = (1/3) * 7.5625 * 2.75
V = (1/3) * 20.796875
V ≈ 6.931 cubic inches

Therefore, the approximate volume of the square pyramid-shaped holiday ornament is approximately 6.93 cubic inches.