The volume of a cone is 78.6 cm^3. If its height is 6 cm, what is the base?
Please explain each step
V = 1/3 Bh
78.6 cm^3 = 1/3 B(6 cm)
B = 39.3 cm^2
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どうもありがとうございます！
Volume of a cone to its height and length of its base
To find the base of a cone, we need to use the formula for the volume of a cone:
Volume = (1/3) * π * r² * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the base
- h is the height of the cone
In this case, we are given that the volume is 78.6 cm³ and the height is 6 cm. We need to find the radius (r), and from that, we can calculate the base.
1. Rearrange the formula to solve for the radius (r):
Volume = (1/3) * π * r² * h
Multiply both sides by 3:
3 * Volume = π * r² * h
Divide both sides by (π * h):
(3 * Volume) / (π * h) = r²
2. Substitute the known values into the equation:
(3 * 78.6 cm³) / (3.14159 * 6 cm) = r²
Simplify:
(235.8 cm³) / (18.84954 cm) = r²
r² ≈ 12.5084 cm²
3. Find the square root of both sides to solve for r:
√(r²) ≈ √(12.5084 cm²)
r ≈ 3.538 cm
4. Now that we know the radius (r), we can find the base of the cone:
The base is simply the diameter of the circular base, which is equal to 2 times the radius:
Base = 2 * r
Base = 2 * 3.538 cm
Base ≈ 7.076 cm
Therefore, the base of the cone is approximately 7.076 cm.