Math - How to find the volume of a sphere

Find the volume of the following sphere.

Sphere

$288 \pi m^3$

$270 \pi m^3$

$300 \pi m^3$

$312 \pi m^3$

$360 \pi m^3$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3} \pi r^3$

where is the radius of the sphere.

Plugging in our values, we get:

$V=\frac{4}{3} \pi (6m)^3$

$V=\frac{4}{3} \pi 216m^3 = 288 \pi m^3$

What is the volume of a sphere with a diameter of 6 in?

$36\pi\ in^{3}$

$216\pi\ in^{3}$

$108\pi\ in^{3}$

$72\pi\ in^{3}$

$288\pi\ in^{3}$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^{3}$

where = radius. The diameter is 6 in, so the radius will be 3 in.

Find the volume of the following sphere.

Sphere

$972 \pi m^3$

$982 \pi m^3$

$992 \pi m^3$

$962 \pi m^3$

$952 \pi m^3$

Explanation

The formula for the volume of a sphere is:

$V = \frac{4 \pi r^3}{3}$

Where is the radius of the sphere

Plugging in our values, we get:

$V = \frac{4 \pi (9m)^3}{3}$

$V = 972 \pi m^3$

Circle_with_diameter

A typical baseball is in diameter. Find the baseball's volume in cubic centimeters.

$230cm^{3}$

$22984.7cm^{3}$

Not enough information to solve

$1838cm^{3}$

$2786cm^{3}$

Explanation

In order to find the volume of a sphere, use the formula

$V=\frac{4}{3}\pi r^{3}$

We were given the baseball's diameter, $\dpi{100} D=76mm$ , which must be converted to its radius.

$r=\frac{76mm}{2}$

$\rightarrow 38mm$

Now we can solve for volume.

$V=\frac{4}{3}\pi (38mm)^{3}$

$V=\frac{4}{3}\pi (54872mm^{3})$

$V=73162\frac{2}{3}mm^{3}*\pi$

$\rightarrow 229847.30mm^{3}$

Convert to centimeters.

$\dpi{100} \frac{229847.30mm^{3}}{1}*\frac{1cm^{3}}{1000mm^{3}}\approx 230cm^{3}$

If you arrived at $1838cm^{3}$ then you did not convert the diameter to a radius.

What is the volume of a sphere whose radius is .

$17.16in^{3}$

$\dpi{100} 16.17in^{3}$

$\dpi{100} 9.65in^{3}$

Not enough information to solve

$\dpi{100} \dpi{100} 6.59in^{3}$

Explanation

In order to find the volume of a sphere, use the formula

$V=\frac{4}{3}\pi r^{3}$

We were given the radius of the sphere, .Therefore, we can solve for volume.

$\dpi{100} V=\frac{4}{3}\pi (1.6in)^{3}$

$\dpi{100} V=\frac{4}{3}\pi (4.096in^{3})$

$\dpi{100} V=17.16in^{3}$

If you calculated the volume to be $\dpi{100} 9.65in^{3}$ then you multiplied by $\frac{3}{4}$ rather than by $\frac{4}{3}$ .

A solid hemisphere has a radius of length r. Let S be the number of square units, in terms of r, of the hemisphere's surface area. Let V be the number of cubic units, in terms of r, of the hemisphere's volume. What is the ratio of S to V?

$\frac{9}{2r}$

$3r$

$\frac{4r}{3}$

$\frac{9r}{2}$

$\frac{3}{r}$

Explanation

First, let's find the surface area of the hemisphere. Because the hemisphere is basically a full sphere cut in half, we need to find half of the surface area of a full sphere. However, because the hemisphere also has a circular base, we must then add the area of the base.

$S = \frac{1}{2}\cdot$ (surface area of sphere) + (surface area of base)

The surface area of a sphere with radius r is equal to $4\pi r^2$ . The surface area of the base is just equal to the surface area of a circle, which is $\pi r^2$ .

$S=\frac{1}{2}\cdot 4\pi r^2+\pi r^2=2\pi r^2+\pi r^2=3\pi r^2$

The volume of the hemisphere is going to be half of the volume of an entire sphere. The volume for a full sphere is $\frac{4}{3}\pi r^3$ .

$V = \frac{1}{2}\cdot$ (volume of sphere)

$V = \frac{1}{2}\cdot \frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3$

Ultimately, the question asks us to find the ratio of S to V. To do this, we can write S to V as a fraction.

$\frac{S}{V}=\frac{3\pi r^2}{\frac{2}{3}\pi r^3}$

In order to simplify this, let's multiply the numerator and denominator both by 3.

$\frac{S}{V}=\frac{3\pi r^2}{\frac{2}{3}\pi r^3}$ = $\frac{9\pi r^2}{2\pi r^3}=\frac{9}{2r}$

The answer is $\frac{9}{2r}$ .

What is the volume of a sphere with a diameter of ?

$288\pi$

$2304\pi$

$48\pi$

$1152\pi$

$24\pi$

Explanation

The formula for volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

The problem gives us the diameter, however, and not the radius. Since the diameter is twice the radius, or , we can find the radius.

$\frac{12}{2}=r$

Now plug that into our initial equation.

$V=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\pi (6)^3$

$V=\frac{4}{3}\pi(216)$

$V=288\pi$

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate volume of the basketball? Remember that the volume of a sphere is calculated by V=(4πr3)/3

92.48 cu.in.

138.43 cu.in.

434.19 cu.in.

3468.05 cu.in.

8557.46 cu.in.

Explanation

To find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get \[29.5\]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. Then we would plug into the formula for volume V=(4π〖(4.7)〗3) / 3 (The information given of 22 ounces is useless)

What is the volume of a sphere with a radius of ?