Question

Find the volume of a right circular cone that has a height of 4.5 ft and a base with a diameter of 19 ft. Round your answer to the nearest tenth of a cubic foot.

Answer 1

The volume of the right circular cone is approximately 191.1 cubic feet.

Step-by-step explanation:

The volume of a right circular cone can be found using the formula V = (1/3)πr²h, where r is the radius of the cone's base and h is the height.

To find the volume, we first need to find the radius of the cone's base. The diameter of the base is given as 19 ft, so the radius is half of the diameter, which is 19/2 = 9.5 ft.

Substituting the values for radius and height into the formula, we get V = (1/3)π(9.5 ft)²(4.5 ft).

Simplifying this, we get V ≈ 191.1 ft³. Rounded to the nearest tenth, the volume of the cone is approximately 191.1 cubic feet.

Answer 2

425.3 ft

Step-by-step explanation:

\text{Volume of Cone:}

Volume of Cone:

V=\frac{1}{3}\pi r^2h

V=

3

1

​

πr

2

h

\text{Find radius:}

Find radius:

r=\frac{\text{diameter}}{2}=\frac{19}{2}=9.5

r=

2

diameter

​

=

2

19

​

=9.5

h=4.5\hspace{40px}r=9.5

h=4.5r=9.5

Needed information

V=

V=

\,\,\frac{1}{3}\pi r^2h

3

1

​

πr

2

h

V=

V=

\,\,\frac{1}{3}\pi (9.5)^2(4.5)

3

1

​

π(9.5)

2

(4.5)

Plug in

V=

V=

\,\,425.29310548

425.29310548

Evaluate in calculator

V\approx

V≈

\,\,425.3\text{ ft}^3

425.3 ft

3

Round to the nearest tenth