Question

See the picture below

Answer 1

a) 204.20 square centimeters

b) 282.74 square centimeters

c) 314.16 cubic centimeters

Explanation:

a)

The curved surface area of a cone is given by:

Curved Surface Area of Cone =
`\pi rl`

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 =
`\pi rl=\pi (5)(13) = 204.20` square centimeters

b)

Total surface area is curved surface area PLUS the area of the bottom, which is a circle with area
`\pi r^2`

So the bottom has an area of
`\pi r^2 = \pi (5)^2 = 78.54`

Hence, The total surface area = 204.20 + 78.54 = 282.74 square centimeters

c)

The volume of cone is given by
`(1)/(3)\pi r^2 h`

Where radius is 5 and height is 12, so we have:

Volume of Cone =
`(1)/(3)\pi r^2 h = (1)/(3)\pi (5)^2 (12) = 314.16` cubic centimeters