Volume of a Cone = [tex]\frac{\pi r^2 h}{3}[/tex]
Where [tex]r[/tex] is the radius of the cone's base and [tex]h[/tex] is the height of the cone. Find the approximate volume of a cone when [tex]r[/tex] is 4 inches and [tex]h[/tex] is 3 inches.
A. [tex]75 in ^3[/tex]
B. [tex]25 in ^2[/tex]
C. [tex]50 in ^3[/tex]
D. [tex]151 in ^8[/tex]
Answer (2)
Substitute the given radius r = 4 inches and height h = 3 inches into the volume formula V = 3 π r 2 h .
Simplify the expression to V = 16 π .
Approximate π as 3.14159 and calculate the volume: V ≈ 16 × 3.14159 = 50.26544 .
The closest answer from the given options is 50 i n 3 .
Explanation
Problem Analysis and Given Data We are given the formula for the volume of a cone: V = 3 π r 2 h , where r is the radius and h is the height. We are also given that the radius r = 4 inches and the height h = 3 inches. Our goal is to find the approximate volume of the cone.
Substitute Values into Formula Substitute the given values of r and h into the formula: V = 3 π ( 4 2 ) ( 3 ) Simplify the expression: V = 3 π ( 16 ) ( 3 ) = 16 π
Calculate Approximate Volume Approximate the value of π as 3.14159. Then, calculate the approximate volume: V ≈ 16 × 3.14159 = 50.26544
Choose Closest Answer The approximate volume of the cone is 50.26544 cubic inches. Comparing this to the given options, the closest answer is 50 i n 3 .
Examples
Cones are common shapes in everyday life, from ice cream cones to traffic cones. Knowing how to calculate the volume of a cone is useful in many practical situations. For example, if you are filling ice cream cones at a shop, you can use the volume formula to ensure you are dispensing the correct amount of ice cream. Similarly, engineers might use this formula to calculate the amount of material needed to construct a conical structure.
The approximate volume of the cone with a radius of 4 inches and a height of 3 inches is about 50.26544 cubic inches. The closest answer from the provided options is C, 50 i n 3 . Therefore, the answer is C.
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