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Question

A cone shows a radius of 6 and hypotenuse or side as 11.

what is the surface area of the cone? use 3.14 for pi and round to the nearest tenth, if necessary

__ square units

Answer 1

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

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

where \( r \) is the radius and \( l \) is the slant height (hypotenuse).

Given:

• Radius \( r = 6 \)
• Slant height \( l = 11 \)
• \( \pi \approx 3.14 \)

Now, plug the values into the formula:

\[ \text{Surface Area} = 3.14 \times 6 (6 + 11) \]

Calculating inside the parentheses first:

\[ 6 + 11 = 17 \]

Now substitute back into the formula:

\[ \text{Surface Area} = 3.14 \times 6 \times 17 \]

Now calculate \( 3.14 \times 6 \):

\[ 3.14 \times 6 = 18.84 \]

Next, we multiply this result by 17:

\[ \text{Surface Area} = 18.84 \times 17 \]

Calculating \( 18.84 \times 17 \):

\[ 18.84 \times 17 = 319.28 \]

Finally, rounding to the nearest tenth:

\[ \text{Surface Area} \approx 319.3 \text{ square units} \]

The surface area of the cone is approximately 319.3 square units.

Answer 2

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

2,383.26 square centimeters
1,354.125 square centimeters
3,689.5 square centimeters
863.5 square centimeters

Answer 3

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

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

where:

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

Given:

• The diameter of the base is 25 cm, so the radius \( r \) is half of that:

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

• The slant height \( l \) is given as 22 cm.

Now substitute these values into the surface area formula:

1. Calculate \( r + l \):

\[ r + l = 12.5 + 22 = 34.5 \]

2. Now use the formula for the surface area:

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

3. First, calculate \( 3.14 \times 12.5 \):

\[ 3.14 \times 12.5 = 39.25 \]

4. Next, multiply this result by \( 34.5 \):

\[ 39.25 \times 34.5 = 1357.625 \]

Thus, the surface area of the cone is approximately:

\[ \text{Surface Area} \approx 1357.625 \text{ square centimeters} \]

Rounding to three decimal places gives:

\[ \text{Surface Area} \approx 1,357.625 \text{ square centimeters} \]

Among the provided options, the closest match is 1,354.125 square centimeters. It appears there may have been rounding differences, but this is the best option based on the calculations.