Answer:
a) 204.20 square centimeters
b) 282.74 square centimeters
c) 314.16 cubic centimeters
Step-by-step explanation:
a)
The curved surface area of a cone is given by:
Curved Surface Area of Cone = [tex]\pi rl[/tex]
Where r is the radius (given as 5) and l is the slant height, the hypotenuse of the right triangle formed (right side) with 5 as base and 12 as height.
We can find the slant height by using pythagorean theorem on the triangle:
12^2 + 5 ^2 = l^2
144 + 25 = l^2
169 = l^2
l = 13
Now,
Curved Surface Area of Cone = [tex]\pi rl=\pi (5)(13) = 204.20[/tex] square centimeters
b)
Total surface area is curved surface area PLUS the area of the bottom, which is a circle with area [tex]\pi r^2[/tex]
So the bottom has an area of [tex]\pi r^2 = \pi (5)^2 = 78.54[/tex]
Hence, The total surface area = 204.20 + 78.54 = 282.74 square centimeters
c)
The volume of cone is given by [tex]\frac{1}{3}\pi r^2 h[/tex]
Where radius is 5 and height is 12, so we have:
Volume of Cone = [tex]\frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (5)^2 (12) = 314.16[/tex] cubic centimeters
