The total surface area of a cone is given by the formula:
Surface Area = πr(r + l)
where r is the radius and l is the slant height.
In this problem, the surface area is given as 625 in.² and the radius is 5 in. Plugging these values into the formula, we can solve for the slant height:
625 = π(5)(5 + l)
Dividing both sides by π(5) gives:
125 = 5(5 + l)
Dividing both sides by 5 gives:
25 = 5 + l
Subtracting 5 from both sides gives:
20 = l
Therefore, the slant height of the cone is 20 inches.
The total surface area of a cone is 625 in.2. If the radius of the cone is 5 in., what is the slant height of the cone? Round the answer to the nearest whole number.(1 point)
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The surface area of a cone is given by the formula:
Surface Area = πr(r + l)
where r is the radius and l is the slant height.
In this problem, the surface area is given as 625 square inches and the radius is 5 inches. Plugging these values into the formula, we can solve for the slant height:
625 = π(5)(5 + l)
Dividing both sides by π(5) gives:
625/(5π) = 5 + l
Dividing both sides by 5 gives:
125/π = 1 + l
Subtracting 1 from both sides gives:
125/π - 1 = l
Using a calculator to evaluate the left side, we find:
125/π - 1 ≈ 39.79
Therefore, the slant height of the cone is approximately 39.79 inches, rounded to the nearest whole number. So, the slant height is 40 inches.
The surface area of a cone is given by the formula:
Surface Area = πr(r + l)
where r is the radius and l is the slant height.
In this problem, the surface area is given as 625 square inches and the radius is 5 inches. Plugging these values into the formula, we can solve for the slant height:
625 = π(5)(5 + l)
Dividing both sides by π(5) gives:
625/(5π) = 5 + l
Dividing both sides by 5 gives:
125/π = 1 + l
Subtracting 1 from both sides gives:
125/π - 1 = l
Using a calculator to evaluate the left side, we find:
125/π - 1 ≈ 39.79
Therefore, the slant height of the cone is approximately 39.79 inches, rounded to the nearest whole number. So, the slant height is 40 inches.