What is the surface area, in square inches, of a cone with a radius of 10 inches and a slant height of 15 inches? Use 3.14 for pi.

Question

1,177.5 square inches
1,177.5 square inches

785 square inches
785 square inches

2,198 square inches
2,198 square inches

471 square inches

Answer 1

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

\[ \text{Surface Area} = \pi r (r + l) \]

where \( r \) is the radius, \( l \) is the slant height, and \( \pi \) is approximately 3.14.

Given:

• Radius \( r = 10 \) inches
• Slant height \( l = 15 \) inches

Now, substitute the values into the formula:

\[ \text{Surface Area} = 3.14 \times 10 \times (10 + 15) \]

First, calculate \( 10 + 15 \):

\[ 10 + 15 = 25 \]

Now substitute that back into the surface area formula:

\[ \text{Surface Area} = 3.14 \times 10 \times 25 \]

Next, calculate \( 10 \times 25 \):

\[ 10 \times 25 = 250 \]

Now, multiply by \( \pi \):

\[ \text{Surface Area} = 3.14 \times 250 \]

Calculating \( 3.14 \times 250 \):

\[ 3.14 \times 250 = 785 \]

Therefore, the surface area of the cone is:

\[ \text{Surface Area} = 785 \text{ square inches} \]

The correct answer is:

785 square inches.

Answer 2

Use the image to answer the question.

A cone shows a base diameter of 25 centimeters, perpendicular height from the base to the top vertex at 90 degrees, and 22 centimeters as the hypotenuse or the side of the cone.

What is the surface area of the cone? Use 3.14 for pi.

(1 point)
Responses

3,689.5 square centimeters
3,689.5 square centimeters

1,354.125 square centimeters
1,354.125 square centimeters

863.5 square centimeters
863.5 square centimeters

2,383.26 square centimeters
2,383.26 square centimeters
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Answer 3

To find the surface area of the cone, we use the formula:

\[ \text{Surface Area} = \pi r (r + l) \]

where \( r \) is the radius, \( l \) is the slant height, and \( \pi \) is approximately 3.14.

Given Data:

• The diameter of the base is 25 centimeters. Thus, the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{25}{2} = 12.5 \text{ centimeters} \]

• The height of the cone (perpendicular height) is 22 centimeters (given as the hypotenuse, or in this case, the slant height):

\[ l = 22 \text{ centimeters} \]

Now substitute the values into the formula:

\[ \text{Surface Area} = \pi r (r + l) = 3.14 \times 12.5 \times (12.5 + 22) \]

First, calculate \( 12.5 + 22 \):

\[ 12.5 + 22 = 34.5 \]

Now substitute that back into the surface area formula:

\[ \text{Surface Area} = 3.14 \times 12.5 \times 34.5 \]

Next, calculate \( 12.5 \times 34.5 \):

\[ 12.5 \times 34.5 = 431.25 \]

Now, multiply by \( \pi \):

\[ \text{Surface Area} = 3.14 \times 431.25 \]

Calculating \( 3.14 \times 431.25 \):

\[ 3.14 \times 431.25 \approx 1,354.125 \]

Thus, the surface area of the cone is approximately:

\[ \text{Surface Area} \approx 1,354.125 \text{ square centimeters} \]

The correct answer is:

1,354.125 square centimeters.

Answer 4

A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 for pi.(1 point)
Responses

197.82 square centimeters
197.82 square centimeters

452.16 square centimeters
452.16 square centimeters

339.12 square centimeters
339.12 square centimeters

1,356.48 square centimeters

Answer 5

To find the surface area of a cone, we can use the formula:

\[ \text{Surface Area} = \pi r (r + l) \]

where

• \( r \) is the radius,
• \( l \) is the slant height, and
• \( \pi \) is approximately 3.14.

Given Data:

• Radius \( r = 6 \) centimeters
• Slant height \( l = 18 \) centimeters

Substitute the values into the formula:

\[ \text{Surface Area} = \pi r (r + l) = 3.14 \times 6 \times (6 + 18) \]

First, calculate \( 6 + 18 \):

\[ 6 + 18 = 24 \]

Now substitute back into the surface area formula:

\[ \text{Surface Area} = 3.14 \times 6 \times 24 \]

Next, calculate \( 6 \times 24 \):

\[ 6 \times 24 = 144 \]

Now, multiply by \( \pi \):

\[ \text{Surface Area} = 3.14 \times 144 \]

Calculating \( 3.14 \times 144 \):

\[ 3.14 \times 144 = 452.16 \]

Thus, the surface area of the spyglass is:

\[ \text{Surface Area} = 452.16 \text{ square centimeters} \]

The correct answer is:

452.16 square centimeters.

Answer 6

A designer is creating a modern art sculpture of an hourglass out of steel, to be on display at the town library. The hourglass is made by two cones meeting at the top point. The designer wants to know how many square feet of steel is needed for the outside of the sculpture, if the slant height of each cone is 5 feet and the diameter is 8 feet. Use 3.14 for pi.(1 point)
Responses

113.04 square feet
113.04 square feet

226.08 square feet
226.08 square feet

653.12 square feet
653.12 square feet

326.56 square feet

Answer 7

To find the surface area of the hourglass sculpture made of two cones, we can calculate the surface area of one cone and then multiply by two since the hourglass consists of two identical cones.

Surface Area of One Cone

The formula for the lateral (outside) surface area of a cone is:

\[ \text{Surface Area} = \pi r l \]

where:

• \( r \) is the radius,
• \( l \) is the slant height,
• \( \pi \) is approximately 3.14.

Given Data:

• Diameter = 8 feet, so the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \text{ feet} \]

• Slant height \( l = 5 \) feet.

Calculate the Surface Area of One Cone:

Substituting the values into the formula:

\[ \text{Surface Area} = 3.14 \times 4 \times 5 \]

First, calculate \( 4 \times 5 \):

\[ 4 \times 5 = 20 \]

Now multiply by \( \pi \):

\[ \text{Surface Area} = 3.14 \times 20 = 62.8 \text{ square feet} \]

Total Surface Area for Two Cones:

Since the hourglass consists of two cones, we multiply the surface area of one cone by 2:

\[ \text{Total Surface Area} = 2 \times 62.8 = 125.6 \text{ square feet} \]

However, it's important to note that the hourglass does not have the base areas (open at the top and bottom). Each cone's base is not part of the surface area.

Hence, the surface area required for the outside of the sculpture is:

\[ \text{Total Surface Area} = 125.6 \text{ square feet} \]

Therefore, the surface area needed for the steel is:

The response options do not include 125.6 square feet, but it seems there might be a misunderstanding. Let's clarify:

Since one cone's surface area is \( 62.8 , \text{square feet} \) and we are covering both cones fully,

• The material required for two cones would typically include the area we calculated (lateral surface) only would lead us back to the already provided options selection.

Double-checking gives/scaled an interpretation via area gathering up; maintaining only lateral visibility still remains a concern.

None of the options (113.04, 226.08, 653.12, 326.56) directly correlate with two lateral calculation reliance strictly.

If the assumption and options reflect through perhaps further contextual application (like exterior painting or visibilities) need elucidation.

Given that understanding:

Since options don’t quite represent re-factoring the overall, closest passages implied represent through readiness allows verification.

Additional Confirmation: Please confirm context is accurately outlined or reassess navigating the cone's aspect clearly on distinct areas needed duplicitously.