Answer:
Explanation:
The cylinder has the greater volume because the cylinder fits within the rectangular prism with extra space between the two figures.
What is a prism?
A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
We can see this by comparing the formulas for the volumes of the two shapes.
The volume V of a rectangular prism with length L, width W, and height H is given by:
V = L x W x H
The volume V of a cylinder with radius r and height H is given by:
V = πr²H
Now,
We are told that the length of each side of the prism base is equal to the diameter of the cylinder.
Since the diameter is twice the radius, this means that the width and length of the prism base are both equal to twice the radius of the cylinder.
So we can write:
L = 2r
W = 2r
Substituting these values into the formula for the volume of the rectangular prism, we get:
V prism = L x W x H
V prism = 2r x 2r x H
V prism = 4r²H
Substituting the radius and height of the cylinder into the formula for its volume, we get:
V cylinder = πr^2H
To compare the volumes,
We can divide the volume of the cylinder by the volume of the prism:
V cylinder / V prism = (πr²H) / (4r²H)
V cylinder / V prism = π/4
π/4 is greater than 1/1,
Thus,
The cylinder has a greater volume.
The cylinder fits within the rectangular prism with extra space between the two figures because the cylinder is inscribed within the prism, meaning that it is enclosed within the prism but does not fill it completely.