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sukhopar [10]
4 years ago
10

Given a rectangular pyramid and a rectangular prism that have the same base and same height, how do their volumes compare? If th

e pyramid was full of water, how much of the prism would it fill up? Name another pair of three-dimensional objects that have a relationship similar to this.
Mathematics
1 answer:
Evgen [1.6K]4 years ago
3 0

Answer:

Part 1) The volume of the prism is 3 times greater than the volume of the pyramid

Part 2) The prism would fill only one-third

Part 3) The cylinder and the cone

Step-by-step explanation:

Part 1) How do their volumes compare?

we know that

The volume of a rectangular prism is equal to

Vprism=BH

where

B is the area of the base of rectangular prism

H is the height of the prism

The volume of a rectangular pyramid is equal to

Vpyramid=\frac{1}{3}BH

where

B is the area of the base of rectangular pyramid

H is the height of the pyramid

Compare the volumes

Vprism=BH -----> equation A

Vpyramid=\frac{1}{3}BH -----> equation B

substitute equation A in equation B

Vpyramid=\frac{1}{3}Vprism

Vprism=(3)Vpyramid

The volume of the prism is 3 times greater than the volume of the pyramid

Part 2) If the pyramid was full of water, how much of the prism would it fill up?

Remember that

Vpyramid=\frac{1}{3}Vprism

therefore

The prism would fill only one-third

Part 3) Name another pair of three-dimensional objects that have a relationship similar to this

we have the cylinder and the cone

The volume of the cylinder is equal to

Vcylinder=\pi r^{2}h

The volume of the cone is equal to

Vcone=\frac{1}{3}\pi r^{2}h

Compare the volumes

Vcylinder=(3)Vcone

The volume of the cylinder is 3 times greater than the volume of the cone

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