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. (1 point)
• 471 square inches
• 2,198 square inches
• 1,177.5 square inches
• 785 square inches
The surface area of a cone is given by the formula:
A = πr(r + l)
where r is the radius and l is the slant height.
Given that the radius is 10 inches and the slant height is 15 inches, we can plug these values into the formula to calculate the surface area:
A = 3.14 * 10(10 + 15)
= 3.14 * 10 * 25
= 785 square inches
Therefore, the surface area of the cone is 785 square inches.
The correct answer is: • 785 square inches.
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)
• 339.12 square centimeters
• 1,356.48 square centimeters
• 197.82 square centimeters
452.16 square centimeters
The surface area of a cone is given by the formula:
A = πr(r + l)
where r is the radius and l is the slant height.
Given that the radius is 6 centimeters and the slant height is 18 centimeters, we can plug these values into the formula to calculate the surface area:
A = 3.14 * 6(6 + 18)
= 3.14 * 6 * 24
= 452.16 square centimeters
Therefore, the surface area of the spyglass is 452.16 square centimeters.
The correct answer is: • 452.16 square centimeters.
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)
• 653.12 square feet
• 326.56 square feet
• 113.04 square feet
• 226.08 square feet
The surface area of a cone is given by the formula:
A = πr(r + l)
where r is the radius and l is the slant height.
Given that the slant height is 5 feet, we can find the radius by dividing the diameter by 2:
radius = 8 feet / 2 = 4 feet
Plugging these values into the surface area formula, we can calculate the surface area of one cone:
A = 3.14 * 4(4 + 5)
= 3.14 * 4 * 9
= 113.04 square feet
Since there are two cones, we need to double this value to get the total surface area of the sculpture:
Total surface area = 2 * 113.04 square feet
= 226.08 square feet
Therefore, the designer will need 226.08 square feet of steel for the outside of the sculpture.
The correct answer is: • 226.08 square feet.
A cone-shaped megaphone has a radius of 15 centimeters and a slant height of 20 centimeters. A megaphone has an open bottom. What is the lateral surface area of the megaphone, in square centimeters? Use 3.14 for pi. (1 point)
• 1,648.5 square centimeters
• 1,884 square centimeters
• 942 square centimeters
• 109.9 square centimeters
The lateral surface area of a cone is given by the formula:
A = πr(l)
where r is the radius and l is the slant height.
Given that the radius is 15 centimeters and the slant height is 20 centimeters, we can plug these values into the formula to calculate the lateral surface area:
A = 3.14 * 15 * 20
= 942 square centimeters
Therefore, the lateral surface area of the megaphone is 942 square centimeters.
The correct answer is: • 942 square centimeters.