Find the volume of a right circular cone that has a height of 9m and a base with a circumference of 19.6m . Round your answer to the nearest tenth of a cubic foot .

Answers

Answer 1

Answer:

x = 3.0 cubic foot.

Explanation:

Given the following data;

Height = 9m

Circumference of base = 19.6m

To find the volume of right circular cone;

First of all, we would determine the radius of the circular base.

Circumference of circle = 2πr

19.6 = 2*3.142*r

19.6 = 6.284r

Radius, r = 19.6/6.284

Radius, r = 3.12 m

Mathematically, the volume of a right circular cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the formula, we have;

[tex] V = \frac{1}{3} * 3.142 * 3.12^{2} * 9 [/tex]

[tex] V = 3.142 * 3.12^{2} * 3 [/tex]

[tex] V = 9.426 * 9.7344 [/tex]

V = 91.7565

Converting to foot;

1 foot = 30.48 cm

x foot = 91.7565 cm

Cross-multiplying, we have;

91.7565 = 30.48x

x = 91.7565/30.48

x = 3.0104

x = 3.0 (to the nearest cubic foot).

Answer 2

Answer:

x = 3.0 cubic foot.

Explanation:

Given the following data;

Height = 9m

Circumference of base = 19.6m

To find the volume of right circular cone;

First of all, we would determine the radius of the circular base.

Circumference of circle = 2πr

19.6 = 2*3.142*r

19.6 = 6.284r

Radius, r = 19.6/6.284

Radius, r = 3.12 m

Mathematically, the volume of a right circular cone is given by the formula;

V = 1/3pir^2h

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Converting to foot;

1 foot = 30.48 cm

x foot = 91.7565 cm

Cross-multiplying, we have;

91.7565 = 30.48x

x = 91.7565/30.48

x = 3.0104

x = 3.0 (to the nearest cubic foot).

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