b The volume of the square prism is greater than the volume of the cylinder. See solution for the explanation.
C
c Multiplying the radius by x will affect more than multiplying the height by x. See solution for the explanation.
Practice makes perfect
a We are asked to draw a right cylinder and an oblique cylinder with a height of 10 meters and a diameter of 6 meters. Remember that if the side of a cylinder is not perpendicular to its top and bottom, the cylinder is said to be oblique.
B represents the area of the base and h represents the height of a figure. Therefore, if two solids have the same height the one with the greater base area has the greater volume. We are given a square prism with the height of 10 meters, and a base edge of 6 meters. We are asked to compare its volume with the volume of the cylinder from Part A.
As we can see, the area of the square is greater than the area of the circle. This tells us that the volume of the square prism is greater than the volume of the cylinder.
c We are asked to find which change affects the volume of the cylinder more: multiplying the height by x, or multiplying the radius by x. Let r and h denote the radius and the height of the cylinder, respectively.
The volume of the cylinder is \textcolor{darkorange}{V_\text{c}}=\textcolor{darkorange}{\pi r^2h}. Now, let's find out how the multiplying by x would affect the volume of the cylinder.
Multiplying
Radius
Height
Radius
rx
r
Height
r
hx
Volume
V=π* Radius^2* Height
π ( rx)^2 h=x^2*π r^2h=x^2*V_c
π r^2( hx)=x*π r^2h=x*V_c
If we multiply the radius of a cylinder by x, its volume is x^2 times larger. If we multiply the height of a cylinder by x, its volume is x times larger. This tells us that multiplying the radius will affect the volume more than multiplying the height.
