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2 months ago

A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.

Mathematics

2 answers:

tester [12.3K]2 months ago

7 0

Answer:

The accurate statements are:

The sphere has a diameter of 32 inches.

The length of the radius is half that of the diameter.

The sphere's volume totals StartFraction 16,384 Over 3 EndFraction pi cubic inches.

Step-by-step explanation:

The sphere has a diameter of 8 in. False

This is incorrect because the radius is always half the diameter. Half of 8 in gives 4 in, whereas the stated radius is 16 in.

The sphere’s volume is StartFraction 2,048 Over 3 EndFraction pi cubic inches. False

This is incorrect since the formula for a sphere's volume is 4πr³/3 = (16,384/3) π cubic inches.

The sphere has a diameter of 32 in. True

This is correct as the radius is half the diameter. Half of 32 in is 16 in, aligning with the given radius.

The length of the radius is half that of the diameter. True

This is accurate because the radius, by definition, is half of the diameter.

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi cubic inches. True

This is correct based on the volume calculation of 4πr³/3 = (16,384/3) π cubic inches.

The diameter is half the radius's length. False

Instead, it is the radius that measures half the diameter’s length.

lawyer [12.5K]2 months ago

6 0

Answer:

The sphere has a 32 in. diameter. CORRECT: A sphere's diameter equals twice its radius; therefore, if the radius is 16, then the diameter is 32.
The radius measures half the diameter's length. CORRECT: According to the definition, the diameter represents the greatest distance across the sphere, and its length is twice the radius since the radius extends from the center to the surface (imagining that distance across the sphere can connect two radii, which create the diameter).
The sphere's volume (V) can be computed as $\frac{4\pi r^3}{3}$ , where r is the radius. In this instance, the sphere's volume equals $\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}$ , which can also be expressed as $\frac{16384\times\pi}{3}$ .

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Answer:

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Step-by-step explanation:

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Consequently:

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The selected choice is A.

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Step-by-step explanation:

Extracting essential details from the query:-

*** A fish tank has a volume of 4710 inches^3

*** The tank owner utilizes a cylindrical bucket for filling the tank

*** The bucket has a radius of 5 inches and a height of 20 inches

*** We need to compute how many times Gus has to fill the bucket to fully fill the fish tank.

Since the container used for filling the tank is cylindrical, we will apply the formula for finding a cylinder's volume to derive the bucket's volume used for filling the tank.

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