The formula gives the volume [tex]$V$[/tex] of a right circular cone with radius [tex]$r$[/tex] and height [tex]$h$[/tex]. What is the volume, in cubic meters, of a right circular cone with a radius of 4 meters and a height of 3 meters?
A. [tex]$16 \pi$[/tex]
B. [tex]$36 \pi$[/tex]
C. [tex]$48 \pi$[/tex]
D. [tex]$144 \pi$[/tex]
Answer (2)
Substitute the given radius r = 4 meters and height h = 3 meters into the volume formula: V = 3 1 π r 2 h .
Calculate r 2 = 4 2 = 16 .
Multiply the values: V = 3 1 π ( 16 ) ( 3 ) = 3 1 π ( 48 ) .
Divide by 3: V = 16 π cubic meters. The volume of the cone is 16 π .
Explanation
Problem Analysis We are given the formula for the volume of a right circular cone: V = 3 1 π r 2 h , where r is the radius and h is the height. We are given that the radius r = 4 meters and the height h = 3 meters. Our goal is to find the volume V in cubic meters.
Substitute Values Now, we substitute the given values of r and h into the formula: V = 3 1 π ( 4 2 ) ( 3 )
Calculate Square First, we calculate 4 2 = 16 . So the equation becomes: V = 3 1 π ( 16 ) ( 3 )
Multiply Next, we multiply 16 by 3: 16 × 3 = 48 So, V = 3 1 π ( 48 )
Divide Finally, we divide 48 by 3: 3 48 = 16 So, V = 16 π cubic meters.
Final Answer Therefore, the volume of the right circular cone is 16 π cubic meters.
Examples
Cones are not just theoretical shapes; they appear everywhere in real life! Think of ice cream cones, traffic cones, or even the conical roofs of some buildings. Knowing how to calculate the volume of a cone is super useful in many practical situations. For example, if you're filling ice cream into a cone, you'd want to know its volume to avoid overfilling it. Similarly, engineers use these calculations when designing structures or containers in the shape of a cone. The formula V = 3 1 π r 2 h helps us determine exactly how much space is inside a cone, based on its radius and height.
The volume of the right circular cone with a radius of 4 meters and a height of 3 meters is 16 π cubic meters. Thus, the correct answer is option A: 16 π .
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