Let’s learn how to determine the volume of a cone.
What is a Cone?
A cone is a three-dimensional object that has a circular base; a vertex or top; a height which is the perpendicular distance from the vertex to the base; and a slant height which refers to the distance from the vertex to the side and down to any point on the base circumference. The radius of the cone’s base is essential to finding the cone’s volume, which is defined as the amount of space an object occupies. Volume is measured in cubic units like cubic inch (in3), cubic feet (ft3), cubic centimeter (cm3), or cubic meter (m3).
To find the volume of a cone, multiply the product of the cone’s base and height by one-third, as expressed in the following formula:
V= 1/3 Bh or V = 1/3 πr²h
where B (Base) = πr² and h= height
Related Reading: Volume of a Cylinder – Formula & Examples
How to Find the Volume of a Cone:
Step 1. Write down the given figures. Make sure the radius and height use the same measurement units. If not, convert either of them to match the other.
Step 2. Plug the given figures into the formula.
Step 3. Perform the operations: multiplication and division. Write the cubic unit together with the answer.
Example #1: Find the Volume of a Cone when given Height & Radius
Find the volume of the cone below.
Solution for Example #1:
Step 1. Write down the given figures, which are the radius (r = 8cm) and height (h = 16cm).
Step 2. Substitute 8cm for r and 16cm for h.
V = 1/3 πr²h
V = 1/3 π(8cm)²(16cm)
Step 3. Simplify.
V = 1/3 π(64cm²)(16cm)
V = 1/3 π(1,024cm3) ≈ 1,071.78…cm3
Therefore, the volume of the cone is about 1,072 cm3.
Example #2: Find the Volume of a Cone when Unit Measurement is Different
Solution for Example #2:
Step 1. Write down the given figures, which are the radius (r = 150cm) and height (h = 2m). Since they differ in measurement units, convert either of them to match the other. Let’ convert 150 cm to meters.
You may recall that 1m = 100 cm
To convert 150cm to m, multiply it by the fraction:
1m / r = 100 cm / 150cm
Cross multiply to solve for r
100 cm (r) = 150 cm (1m)
r = 150/100 m
r = 1.5 m
Therefore, the converted radius is 1.5 m.
Step 2. Substitute 1.5m for r and 2m for h.
V = 1/3 πr²h
V = 1/3 π(1.5m)²(2m)
Step 3. Simplify.
V = 1/3 π(2.25 m²)(2m)
V = 1/3 π(4.5m3) ≈ 4.71m3
Therefore, the volume of the cone is about 4.7m3.
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the volume of a cone.
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