The volume of a right circular cone is determined by the following formula:
V = 1/3πr²h
If the volume of a certain cone is 302cm³ and the height is 8cm, determine the slant height of the cone.
A) 10cm
B) 36cm
C) 12cm
D)24cm
E) 6cm
first find r
V = (1/3) π r^2 h
r^2 = 3 V / (π h)
r^2 = (3*302) / (8 π)
r^2 = 36
so
302 = (1/3) π (36) h = 12 π h
solve for h
V = 1/3πr²h
302 = (1/3)π r^2 (8)
r^2 = 3*302/(8π) = ..
r = 6.004
if slant height is s, then
s^2 = 6^2 + 8^2 = 100
s = 10
Sorry, got distracted, finish it as mathelper did.
To determine the slant height of the cone, we need to use the given volume and height.
The formula for the volume of a right circular cone is:
V = (1/3)πr²h
Given that the volume is 302 cm³ and the height is 8 cm, we can substitute those values into the formula:
302 = (1/3)πr²(8)
To solve for the radius, we need to rearrange the equation:
r² = (3 × 302) / (π × 8)
r² = 1134 / (8π)
Now, we can find the value of r:
r = √(1134 / (8π))
Using a calculator, we find that r ≈ 6.78 cm.
To find the slant height, we can use the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle, with the radius (r) as one side and the height (h) as the other side.
Using the formula:
l = √(r² + h²)
l = √(6.78² + 8²)
l = √(45.92 + 64)
l ≈ √109.92
Using a calculator, we find that l ≈ 10.48 cm.
Since the slant height is approximately 10.48 cm, the closest option in the given choices is A) 10 cm.