Use the formula for the lateral area of a cylinder.
A
about 1000.6 square centimeters
B
The lateral area decreases twice.
Practice makes perfect
We are given that a hot cocoa canister is in the shape of the following cylinder.
We are asked to find the lateral area of the canister. Recall that the lateral area of a cylinder is the circumference of the base times the height. To calculate the lateral area of a cylinder, we can use the following formula.
L.A.=2π rh
In this formula, r is the radius of the base and h is the height of the cylinder. Note that we know the diameter and the height of the cylindrical canister. To find its radius, we can divide the diameter by 2.
Therefore, the radius is equal to 6.5 centimeters. Now, we can substitute the height and the radius into the formula and calculate the lateral area. Let's do it!
We got that the lateral area of the hot cocoa canister is about 1000.6 square centimeters.
Now we want to determine how the lateral area of the canister changes if the height is divided by 2. To do so, let's analyze the two following cylinders.
Recall that we can use the following formula to calculate the lateral area of a cylinder.
L.A.=2π rh
In the formula, r is the radius of the base and h is the height of the cylinder. Using this formula, we can write an expression for the lateral area of each cylinder.
Cylinder
Height, cm
Diameter, cm
Radius, cm
L.A.= 2π r h, cm^2
1
24.5
13
13/2= 6.5
L.A.= 2π ( 6.5) ( 24.5)
2
24.5/2
13
13/2= 6.5
L.A.= 2π ( 6.5) ( 24.5/2)
Notice that we got expressions that are very similar to each other. To compare the lateral areas, we will rewrite the expression for the lateral area of Cylinder 2.
Now we can see that the lateral area of Cylinder 2 is equal to half the lateral area of Cylinder 1.
L.A. of Cylinder 2 = 1/2 * 2π (6.5)(24.5) [0.4em]
⇕ [0.4em]
L.A. of Cylinder 2 = 1/2 * L.A. of Cylinder 1
Therefore, if the height of the container is divided by 2, the lateral area decreases twice.
