A climbing pyramid in a children’s playground has a volume of 440/3 m3. The base is a rectangle, measuring 8 m by 11 m. What is the height of the pyramid?(1 point)

Answer 1

To find the height of the pyramid, we first need to calculate the area of the base of the pyramid:

Area of rectangle = length × width
Area of base = 8 m × 11 m = 88 m2

Now, we can use the formula for the volume of a pyramid:

Volume = (1/3) × base area × height

Substitute the given values:

440/3 = (1/3) × 88 × height

Now, solve for height:

440/3 = 88/3 × height
height = (440/3) / (88/3)
height = 440/88
height = 5

Therefore, the height of the pyramid is 5 meters.

Answer 2

A rectangular prism has a volume of 27 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point) in.3

Answer 3

Given that the rectangular prism has a volume of 27 in^3, and the base and height are congruent in the rectangular pyramid, the volume of the rectangular pyramid can be calculated using the formula for the volume of a pyramid, which is:

Volume = (1/3) × base area × height

Since the base and height of the pyramid are congruent to the rectangular prism, the base area will be the same as the base area of the prism. Let's find the length of each side of the base:

Volume of the rectangular prism = length × width × height
27 in^3 = length × length × length
27 in^3 = length^3

Taking the cube root of both sides to find the length of each side:

length = ∛27
length = 3 in

The base area of the pyramid will be:

Base area = length × length
Base area = 3 in × 3 in
Base area = 9 in^2

Now, we can calculate the volume of the pyramid:

Volume = (1/3) × base area × height
Volume = (1/3) × 9 in^2 × 3 in
Volume = 3 in^3

Therefore, the volume of the rectangular pyramid is 3 in^3.