Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A miniature basketball in the shape of a sphere has a volume of approximately 113 cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?

◻

A miniature basketball in the shape of a sphere has a volume of approximately $113$ cubic inches. What is the length of the basketball's radius, rounded to the nearest inch? $\newline$ ◻

View step-by-step help

View step-by-step help

Circles: word problems

Full solution

Q. A miniature basketball in the shape of a sphere has a volume of approximately

113

cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?

\newline

◻

Volume Formula: We know the volume of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$ , where $V$ is the volume and $r$ is the radius of the sphere. We are given the volume $V = 113$ cubic inches. We need to solve for $r$ .
Rearranging Formula: First, let's rearrange the formula to solve for $r$ . We get $r^3 = \frac{3V}{4\pi}$ .
Substitute Values: Now, we plug in the given volume and the approximate value of $\pi$ into the rearranged formula. Using $\pi \approx 3.14$ , we have $r^3 = \frac{3 \times 113}{4 \times 3.14}$ .
Calculate Value: Let's calculate the value inside the cube root: $r^3 = \frac{339}{12.56}$ .
Cube Root: Performing the division, we find $r^3 \approx 26.9936$ .
Final Radius Calculation: To find the radius $r$ , we take the cube root of $r^3$ . So, $r \approx \sqrt[3]{26.9936}$ .
Final Radius Calculation: To find the radius $r$ , we take the cube root of $r^3$ . So, $r \approx \sqrt[3]{26.9936}$ .Using a calculator, we find that $r \approx 3.00$ inches when rounded to the nearest inch.

More problems from Circles: word problems

Question

Skyler climbs a watchtower to guard against forest fires.

\newline

R(h)=\sqrt{13h}

gives the distance, in kilometers, that Skyler can see when their eyes are

h

meters above the ground.

\newline

A(d)=\pi d^{2}

gives the area, in square kilometers, that Skyler can guard when they can see a distance of

d

\newline

Which expression models the area Skyler can guard when their eyes are

h

meters above the ground?

\newline

1

\newline

13\pi h

\newline

13\pi h^{2}

\newline

\sqrt{13\pi h^{2}}

\newline

169\pi h^{2}

Posted 2 months ago

Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

70\%

. Before the outbreak, the average wait time at the hospital was

m

\newline

Which of the following expressions could represent the average wait time at the hospital after the outbreak?

\newline

2

\newline

0.7m

\newline

\frac{170}{100}m

\newline

m+70

\newline

m+0.7

\newline

1.7m

Posted 1 month ago

Question

The radius of a semicircle is

3

yards. What is the semicircle's area?

\newline

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

Posted 2 months ago

Question

\newline

A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Posted 2 months ago

Question

A quarter is worth

\$0.25

and a half dollar is worth

\$0.50

\newline

a. A quarter has a diameter of

\frac{15}{16}

inch and a height of

\frac{1}{16}

inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.

\newline

b. A half dollar has a diameter of

\frac{9}{8}

inches and a height of

\frac{3}{32}

inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

Posted 2 months ago

Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

8 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

15 \mathrm{~cm}

. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

Find the volume of a right circular cone that has a height of

7.4 \mathrm{~cm}

and a base with a radius of

8.1 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

\mathrm{cm}^{3}

Posted 2 months ago

Question

Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

\mathrm{ft}^{3}

Posted 2 months ago