Question

Consider this sphere with a diameter of 5 m. A sphere with diameter 5 meters. What can be concluded about the sphere? Check all that apply. The sphere has a radius of 10 cm. The diameter measure is substituted into the formula to find the volume. The radius is half the diameter. The formula to apply is V = four-thirds B h The volume of the sphere is two-thirds the volume of a cylinder with the same radius and height.

Answer 1

C

Explanation:

We have a sphere with diameter 5 metres; let's convert this to centimetres by multiplying 5 by 100 because there are 100 cm in 1 m:

5 * 100 = 500 cm

Since the radius is half the diameter, that means the radius is d/2 = 500/2 = 250 cm, which means that A is wrong.

The volume of a sphere is denoted by:
`V=(4)/(3) \pi r^3`, where r is the radius. Nowhere in this equation does "d" for diameter appear, which makes B wrong.

The definition of the radius of a sphere or circle is that it is the distance from the center to a point on the side of the circle/sphere. The diameter is twice of that, which means the radius is half the diameter, making C correct.

As mentioned above, the volume of a sphere is denoted by
`V=(4)/(3) \pi r^3`, which means D is incorrect.

Let's find the volume of a cylinder with the given dimensions: same radius (250 cm) and height (the diameter is equal to height, so height is the same as the radius: 250 cm).

The volume of a cylinder is denoted by:
`V=\pi r^2h`, where r is the radius and h is the height. Plug the values in:

`V=\pi r^2h`

`V=\pi (250)^2*250=250^3*\pi`

The volume of the sphere is:

`V=(4)/(3) \pi r^3`

`V=(4)/(3) \pi (250)^3=(4)/(3) *250^3*\pi`

We can see from comparing these two outcomes that the volume of the sphere is actually 4/3 the volume of the cylinder, so E is incorrect.

The answer is only C.

Answer 2

The radius is half the diameter

The volume of the sphere is two-thirds the volume of a cylinder with the same radius and height.

Explanation:

Radius = 5/2

Volume of the sphere: (4/3)pi × r³

Volume of cylinder: pi × r² × 2r

= 2pi × r³

(4/3)pi × r³ = (2/3)(2pi × r³)