What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? Use 3.14 for pi.(1 point)

Question

Responses

1,570 cubic centimeters
1,570 cubic centimeters

6,280 cubic centimeters
6,280 cubic centimeters

2,355 cubic centimeters
2,355 cubic centimeters

314 cubic centimeters

Answer 1

To find the volume of a cone, you can use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:

• \( V \) is the volume,
• \( r \) is the radius,
• \( h \) is the height,
• \( \pi \) is approximately 3.14.

First, you need to find the radius. The diameter of the cone is 20 cm, so the radius \( r \) is:

\[ r = \frac{diameter}{2} = \frac{20 , \text{cm}}{2} = 10 , \text{cm} \]

Now, plug the radius and height into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (10 , \text{cm})^2 \times 15 , \text{cm \]

Calculating \( (10 , \text{cm})^2 \):

\[ (10 , \text{cm})^2 = 100 , \text{cm}^2 \]

Now substitute that back into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 100 , \text{cm}^2 \times 15 , \text{cm} \]

Calculating:

\[ V = \frac{1}{3} \times 3.14 \times 1500 , \text{cm}^3 \]

Calculating \( 3.14 \times 1500 = 4710 \):

\[ V = \frac{4710}{3} , \text{cm}^3 \]

Calculating \( \frac{4710}{3} = 1570 \):

\[ V = 1570 , \text{cm}^3 \]

Thus, the volume of the cone is 1,570 cubic centimeters.

Answer 2

Use the image to answer the question.

An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.

What is the volume of the cone? Use 3.14 for pi.

(1 point)
Responses

235.5 cubic inches
235.5 cubic inches

942 cubic inches
942 cubic inches

47.1 cubic inches
47.1 cubic inches

423.9 cubic inches
423.9 cubic inches
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Answer 3

To calculate the volume of the cone, we use the formula for the volume of a cone:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:

• \( V \) is the volume,
• \( r \) is the radius,
• \( h \) is the height,
• \( \pi \) is approximately 3.14.

Given:

• Base radius \( r = 9 \) inches,
• Perpendicular height \( h = 5 \) inches.

Now substitute these values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (9^2) \times 5 \]

Calculating \( 9^2 \):

\[ 9^2 = 81 \]

Now plug that back into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 81 \times 5 \]

Calculating \( 81 \times 5 \):

\[ 81 \times 5 = 405 \]

Now substitute that into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 405 \]

Calculating \( 3.14 \times 405 \):

\[ 3.14 \times 405 = 1277.7 \]

Now divide by 3:

\[ V = \frac{1277.7}{3} = 425.9 \]

Thus, the volume of the cone is approximately 423.9 cubic inches.

Answer 4

A professional baker uses a chocolate mold to make decorations for cakes. One chocolate mold is in the shape of a cone and has a diameter of 2 cm and a height of 6 cm. What volume of chocolate, in cubic centimeters, is needed to make a solid chocolate cone? Use 3.14 for π
.(1 point)
Responses

37.68 cubic centimeters
37.68 cubic centimeters

6.28 cubic centimeters
6.28 cubic centimeters

18.84 cubic centimeters
18.84 cubic centimeters

12.56 cubic centimeter

Answer 5

To find the volume of a cone, you can use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:

• \( V \) is the volume,
• \( r \) is the radius of the base,
• \( h \) is the height of the cone,
• \( \pi \) is approximately 3.14.

Given:

• The diameter of the cone is 2 cm, so the radius \( r \) is:

\[ r = \frac{diameter}{2} = \frac{2 , \text{cm}}{2} = 1 , \text{cm} \]

• The height \( h \) is 6 cm.

Now, substitute the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (1 , \text{cm})^2 \times 6 , \text{cm} \]

Calculating \( (1 , \text{cm})^2 \):

\[ (1 , \text{cm})^2 = 1 , \text{cm}^2 \]

Now substitute that back into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 1 , \text{cm}^2 \times 6 , \text{cm} \]

Calculating:

\[ V = \frac{1}{3} \times 3.14 \times 6 = \frac{18.84}{3} \]

Now do the division:

\[ V = 6.28 , \text{cm}^3 \]

Thus, the volume of chocolate needed to make a solid chocolate cone is 6.28 cubic centimeters.