A rectangular prism has a volume of 252 in.3. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
Since the rectangular prism has a volume of 252 in³, we know that:
length x width x height = 252
Let's call the length, width, and height of the rectangular prism "l", "w", and "h", respectively. Then we have:
lwh = 252
Now, the rectangular pyramid has a base and height congruent to the rectangular prism. This means that the base of the pyramid is a rectangle with length "l" and width "w", and the height of the pyramid is also "h". The formula for the volume of a pyramid is:
(1/3) x base area x height
The base area of the pyramid is lw, and the height of the pyramid is also h. So we have:
(1/3) x lw x h
Substituting lwh = 252, we get:
(1/3) x (l x w) x h = (1/3) x base area x height = (1/3) x 252 = 84
Therefore, the volume of the rectangular pyramid is 84 in³.
Since the rectangular prism has a base area of 25 in² and a volume of 125 in³, we can use the formula for the volume of a rectangular prism:
V = base area x height
Substituting 25 in² for the base area and 125 in³ for the volume, we get:
125 = 25 x height
Simplifying and solving for the height, we get:
height = 125/25 = 5 in
Since the rectangular pyramid has a congruent base and height congruent to the prism, the height of the pyramid is also 5 in.
Answer: 5 in.
Answer: 84 in³
To solve this problem, we need to use the fact that a rectangular pyramid has one-third the volume of a rectangular prism with a congruent base and height. So, if the rectangular pyramid has a volume of 10 cm³, the rectangular prism must have a volume that is three times as large, or:
3 x 10 cm³ = 30 cm³
Therefore, the volume of the rectangular prism is 30 cm³.
Answer: 30 cm³.
A rectangular prism has a base area of 25 in.2 and a volume of 125 in.3. If a rectangular pyramid has a congruent base and height congruent to the prism, what is the height of the pyramid?
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A rectangular prism has a base area of 25 in.2 and a volume of 125 in.3. If a rectangular pyramid has a congruent base and height congruent to the prism, what is the height of the pyramid?
A rectangular prism has a base area of 25 in.2 and a volume of 125 in.3. If a rectangular pyramid has a congruent base and height congruent to the prism, what is the height of the pyramid?(1 point)
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