A foam cylinder, with a diameter of 3 inches and height of 4 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the hundredths place.
A. $9.42 in ^3$
B. $14.14 in ^3$
C. $28.27 in ^3$
D. $37.70 in ^3$

Question

GinnyAnswer · Answer

Determine the radius of the cone: r = 2 3 ​ = 1.5 inches. 
 Identify the height of the cone: h = 4 inches. 
 Calculate the volume of the cone using the formula: V = 3 1 ​ π r 2 h = 3 1 ​ π ( 1.5 ) 2 ( 4 ) = 3 π . 
 Approximate the volume to the hundredths place: V ≈ 9.42 cubic inches. 
 
 9.42 i n 3 ​ 
 Explanation 
 
 Problem Analysis We are given a foam cylinder with a diameter of 3 inches and a height of 4 inches. Our goal is to find the maximum volume of a cone that can be carved from this cylinder. The maximum volume of the cone will occur when the cone has the same base and height as the cylinder. 
 
 Find Radius The radius of the cylinder (and the cone) is half of the diameter. Therefore, the radius r is: r = 2 3 ​ = 1.5 inches The height h of the cylinder (and the cone) is given as: h = 4 inches 
 
 Calculate Volume The volume V of a cone is given by the formula: V = 3 1 ​ π r 2 h Substituting the values of r and h into the formula, we get: V = 3 1 ​ π ( 1.5 ) 2 ( 4 ) V = 3 1 ​ π ( 2.25 ) ( 4 ) V = 3 1 ​ π ( 9 ) V = 3 π 
 
 Approximate and Round Using the value of π ≈ 3.14159 , we can calculate the volume: V = 3 × 3.14159 ≈ 9.42477 Rounding the volume to the hundredths place, we get: V ≈ 9.42 cubic inches 
 
 Final Answer The maximum volume of the cone that can be carved from the cylinder is approximately 9.42 cubic inches.

Examples 
 Imagine you're designing ice cream cones. You want to know the maximum amount of ice cream you can fit into a cone that's carved out from a cylindrical block of frozen ice cream. Knowing how to calculate the maximum volume helps you avoid waste and optimize the size of the ice cream portion.

Anonymous · Answer

The maximum volume of the cone that can be carved from the foam cylinder is approximately 9.42 cubic inches. This is calculated using the formula for the volume of a cone with radius 1.5 inches and height 4 inches. The correct answer is A. 9.42 in³. 
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A foam cylinder, with a diameter of 3 inches and height of 4 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the hundredths place. A. $9.42 in ^3$ B. $14.14 in ^3$ C. $28.27 in ^3$ D. $37.70 in ^3$

Answer (2)

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A foam cylinder, with a diameter of 3 inches and height of 4 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the hundredths place.
A. $9.42 in ^3$
B. $14.14 in ^3$
C. $28.27 in ^3$
D. $37.70 in ^3$