A cylinder has a volume of $288 \pi$ cubic meters and a height of 9 meters. What is the area of the base?
A. $32 \pi$ square meters
B. $18 \pi$ square meters
C. $279 \pi$ square meters
D. $2,592 \pi$ square meters
Answer (2)
Recall the formula for the volume of a cylinder: V = A × h .
Substitute the given values: 288 π = A × 9 .
Solve for the area of the base: A = 9 288 π .
Calculate the area: A = 32 π square meters. The area of the base is 32 π .
Explanation
Problem Analysis We are given a cylinder with a volume of 288 π cubic meters and a height of 9 meters. We need to find the area of the base of the cylinder.
Volume Formula The volume V of a cylinder is given by the formula: V = A × h where A is the area of the base and h is the height of the cylinder.
Substitute Values We are given that V = 288 π cubic meters and h = 9 meters. Substituting these values into the formula, we get: 288 π = A × 9
Solve for Area To find the area of the base A , we need to solve for A in the equation above. Divide both sides of the equation by 9: A = 9 288 π A = 32 π
Final Answer Therefore, the area of the base of the cylinder is 32 π square meters.
Examples
Cylinders are commonly found in everyday life, from cans of soup to water tanks. Knowing how to calculate the base area of a cylinder given its volume and height is useful in various practical situations. For example, if you're designing a cylindrical storage container and need it to hold a specific volume, you can use this calculation to determine the required base area. This ensures that your container meets the necessary storage requirements efficiently. The formula V = A × h can be rearranged to A = V / h to find the base area A when the volume V and height h are known.
The area of the base of the cylinder is 32 π square meters, which we calculated using the volume formula for cylinders. We substituted the given values and solved for the area, confirming it is option A. The calculation shows how volume, area, and height are related in a cylinder.
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