QuestionFind the volume of a beach ball with a radius of 30 cm. Use $\pi$ or 3.14 for your answer in $\mathrm{cm}^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The shape of the beach ball is a sphere. The radius of the beach ball is30 cm3. We are asked to find the volume of the sphere, which represents the volume of air the beach ball can hold4. The formula for the volume of a sphere is given by $V = \frac{4}{3}\pi r^{3}$ , where $r$ is the radius of the sphere

STEP 2

First, we need to substitute the given radius into the formula for the volume of a sphere.
$V = \frac{4}{}\pi (30\,cm)^{}$

STEP 3

Calculate the cube of the radius.
$30^3 =27,000\,cm^3$

STEP 4

Substitute the cube of the radius back into the volume formula.
$V = \frac{4}{3}\pi (27,000\,cm^3)$

STEP 5

Calculate the volume of the sphere by multiplying the fraction $\frac{4}{3}$ by $\pi$ and by the cube of the radius.
$V = \frac{4}{3}\pi \times27,000\,cm^3$

STEP 6

Calculate the volume of the sphere.
$V =113,097.335529232\,cm^3$ The volume of air that the beach ball will hold is approximately113,097.335529232 cubic centimeters. If you want an exact answer in terms of $\pi$ , the volume is $\frac{4}{3}\pi \times27,000\,cm^3$ or $36,000\pi\,cm^3$ .

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QuestionFind the volume of a beach ball with a radius of 30 cm. Use $\pi$ or 3.14 for your answer in $\mathrm{cm}^{3}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to substitute the given radius into the formula for the volume of a sphere.
$V = \frac{4}{}\pi (30\,cm)^{}$

STEP 3

Calculate the cube of the radius.
$30^3 =27,000\,cm^3$

STEP 4

Substitute the cube of the radius back into the volume formula.
$V = \frac{4}{3}\pi (27,000\,cm^3)$

STEP 5

Calculate the volume of the sphere by multiplying the fraction $\frac{4}{3}$ by $\pi$ and by the cube of the radius.
$V = \frac{4}{3}\pi \times27,000\,cm^3$

STEP 6

Calculate the volume of the sphere.
$V =113,097.335529232\,cm^3$ The volume of air that the beach ball will hold is approximately113,097.335529232 cubic centimeters. If you want an exact answer in terms of $\pi$ , the volume is $\frac{4}{3}\pi \times27,000\,cm^3$ or $36,000\pi\,cm^3$ .

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QuestionFind the volume of a beach ball with a radius of 30 cm. Use π\piπ or 3.14 for your answer in cm3\mathrm{cm}^{3}cm3.

Studdy Solution

STEP 1

STEP 2

First, we need to substitute the given radius into the formula for the volume of a sphere.V=4π(30 cm)V = \frac{4}{}\pi (30\,cm)^{}V=4​π(30cm)

STEP 3

Calculate the cube of the radius.303=27,000 cm330^3 =27,000\,cm^3303=27,000cm3

STEP 4

Substitute the cube of the radius back into the volume formula.V=43π(27,000 cm3)V = \frac{4}{3}\pi (27,000\,cm^3)V=34​π(27,000cm3)

STEP 5

Calculate the volume of the sphere by multiplying the fraction 43\frac{4}{3}34​ by π\piπ and by the cube of the radius.V=43π×27,000 cm3V = \frac{4}{3}\pi \times27,000\,cm^3V=34​π×27,000cm3

STEP 6

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QuestionFind the volume of a beach ball with a radius of 30 cm. Use $\pi$ or 3.14 for your answer in $\mathrm{cm}^{3}$ .

First, we need to substitute the given radius into the formula for the volume of a sphere.
$V = \frac{4}{}\pi (30\,cm)^{}$

Calculate the cube of the radius.
$30^3 =27,000\,cm^3$

Substitute the cube of the radius back into the volume formula.
$V = \frac{4}{3}\pi (27,000\,cm^3)$

Calculate the volume of the sphere by multiplying the fraction $\frac{4}{3}$ by $\pi$ and by the cube of the radius.
$V = \frac{4}{3}\pi \times27,000\,cm^3$