Question

A sphere with a diameter of 13 inches is shown, which of the following is closest to the volume of the sphere? A. 9203 in ^3 B. 1150 in^3 C. 163 in ^3 D. 82 in ^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of a sphere, you use the formula V = (4/3) * pi * r^3, where r is the radius of the sphere. Since the diameter is given, we first need to find the radius by dividing the diameter by 2: 13 / 2 = 6.5 inches.

Now we can plug the radius into the formula to find the volume:
V = (4/3) * pi * (6.5)^3
V ≈ (4/3) * 3.14159 * 274.625
V ≈ 1153.74 in^3

The closest answer choice to the volume of the sphere is B. 1150 in^3.

Answer 2

The similarity ratio of similar solids is 5:4. The ratio of their surface areas is _______. The ratio of their volumes is _______. Write the ratios with a colon :

Answer 3

[AI-generated answer — Bot GPT 3.5]

When comparing similar solids, the ratio of their surface areas is equal to the square of the similarity ratio, and the ratio of their volumes is equal to the cube of the similarity ratio.

Given that the similarity ratio is 5:4:

Ratio of surface areas: (5/4)^2 = 25:16
Ratio of volumes: (5/4)^3 = 125:64

So, the ratios are:
Ratio of surface areas: 25:16
Ratio of volumes: 125:64

Answer 4

In 00, mAB = 20 and CA = BD. What is mCD?

Answer 5

[AI-generated answer — Bot GPT 3.5]

In order to determine the value of mCD, we need to know more information about the figure or the relationships between the angles. The information provided in the question does not specifically give us a way to determine the measure of angle CD.

To find the measure of angle CD, we need additional information or details about the figure's properties or any additional angles that can help us determine the value of mCD.