Question
Surface area of cone practice correct answers
Answers
GPT 3.5
Here are some correct answers for practice problems involving the surface area of a cone:
1) Find the surface area of a cone with a radius of 5 inches and a slant height of 10 inches.
Solution: The formula for the surface area of a cone is A = πr(r + l), where r is the radius and l is the slant height.
Plugging in the given values, we have:
A = π(5)(5 + 10)
A = π(5)(15)
A = 75π square inches
Therefore, the surface area of the cone is 75π square inches.
2) A cone has a surface area of 100 square centimeters. The radius of the base is 3 centimeters. Find the slant height.
Solution: Rearranging the formula for the surface area of a cone, we have A = πr(r + l), where r is the radius and l is the slant height.
Plugging in the given values, we have:
100 = π(3)(3 + l)
100 = π(3)(3 + l)
To solve for l, divide both sides by π(3):
100/(π(3)) = 3 + l
Simplifying, we have:
33.49 = 3 + l
Subtracting 3 from both sides, we get:
l = 30.49
Therefore, the slant height of the cone is approximately 30.49 centimeters.
1) Find the surface area of a cone with a radius of 5 inches and a slant height of 10 inches.
Solution: The formula for the surface area of a cone is A = πr(r + l), where r is the radius and l is the slant height.
Plugging in the given values, we have:
A = π(5)(5 + 10)
A = π(5)(15)
A = 75π square inches
Therefore, the surface area of the cone is 75π square inches.
2) A cone has a surface area of 100 square centimeters. The radius of the base is 3 centimeters. Find the slant height.
Solution: Rearranging the formula for the surface area of a cone, we have A = πr(r + l), where r is the radius and l is the slant height.
Plugging in the given values, we have:
100 = π(3)(3 + l)
100 = π(3)(3 + l)
To solve for l, divide both sides by π(3):
100/(π(3)) = 3 + l
Simplifying, we have:
33.49 = 3 + l
Subtracting 3 from both sides, we get:
l = 30.49
Therefore, the slant height of the cone is approximately 30.49 centimeters.