MATHEMATICS HIGH SCHOOL

Find the volume of a right circular cone that has a height of 19.4 in and a base with a circumference of 8.3 in. Round your answer to the nearest tenth of a cubic inch.

Answers

Answer 1

Answer:

Answer:

$V=35.4 in^3$

Step-by-step explanation:

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

$V=(1)/(3) \pi r^2h$

where $h=19.4 in$ is the height of the cone.

We can deduce the radius from the circumference of the cone.

$C=2\pi r$

It was given that the circumference is 8.3 in.

$\Rightarrow 8.3=2(3.14) r$

$\Rightarrow 8.3=6.28r$

$\Rightarrow 1.32=r$

The volume of the cone now becomes;

$V=(1)/(3) * 3.14* (1.32)^2* 19.4$

$V=35.380in^3$

The volume of the cone to the nearest tenth is 35.4 cubic inches to the nearest tenth.

Answer 2

Answer:

Final answer:

By calculating the radius from the given circumference, we can find the volume of a right circular cone with the height of 19.4 inches and a base with a circumference of 8.3 inches to be 33.3 cubic inches.

Explanation:

To calculate the volume of a right circular cone, we need to know the radius, r, and the height, h.

The formula to find the volume, V, of a cone is V = 1/3*π*r²*h.

Given that the height, h, is 19.4 inches, we need to find the radius.

Since the given circumference, C, is 8.3 inches and the formula for circumference is 2*π*r, we can calculate the radius. Solving 8.3 inches = 2*π*r for r gives us r≈1.3 inches.

Then, inserting the values of r and h in the volume formula gives V = 1/3*π*(1.3)²*19.4≈ 33.3 cubic inches.

Rounding to the nearest tenth gives the volume as approximately 33.3 in³.

Learn more about Volume of Cone here:

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Answers

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Answers

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Answers

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Answers

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