Mathematics: What is the volume of the cone? use π ≈ 3.14. a. 12.56 cubic units b. 18.84 cubic units c. 20.93 cubic units d. 25.12 cubic units

What is the volume of the cone? use π ≈ 3.14.

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05.01.2022

Option (a) is correct.

The volume of cone is 12.56 cubic meters.

Step-by-step explanation:

Given : A oblique cone with slant height = 5 units and diameter = 4 units.

We have to find the Volume of the given oblique cone.

Consider the given oblique cone with slant height = 5 units and diameter = 4 units.

In a right angle triangle, the square of hypotenuse is equal to the sum of square of base and perpendicular.

that is h^2=b^2+p^2

Apply Pythagoras theorem,

We have,

h = 5 and b = 4

Thus, 5^2=4^2+p^2

Solve for p , we have,

25-16=p^2

9=p^2

Thus, p = 3 (as length cannot be negative)

Thus, the height of cone is 3 units

Volume of cone = $\frac{1}{3}\pi r^2h$

Put r = 2 and h = 3 and π ≈ 3.14.

We have,

Volume of cone = $\frac{1}{3}\cdot 3.14 \cdot 4 \cdot3$

Simplify, we have,

Volume of cone = 12.56 units³

Thus, The volume of cone is 12.56 cubic meters.

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