The surface area of a cone is 55 pie cm squared. The radius is 5 cm. What is the slant height?
To find the slant height of a cone, we'll first need to use the formula for the surface area of a cone, which is:
Surface Area = πr(r + l)
Where:
- Surface Area is the given value (55π cm²)
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the base of the cone (5 cm)
- l is the slant height of the cone (what we need to find)
We can substitute the given values into the formula and solve for l:
55π = π * 5(5 + l)
Simplifying the equation:
55π = 25π + π * 5l
Combining like terms:
55π - 25π = π * 5l
30π = π * 5l
Dividing both sides of the equation by π:
30 = 5l
Finally, solving for l by dividing both sides of the equation by 5:
l = 30 / 5
l = 6 cm
Therefore, the slant height of the cone is 6 cm.