Question

If the diameter of the base of the cone is 4.0 inches and the slant height is 6.0 inches, what is the volume of the ice cream and the area of the waffle that made the cone?

Answer 1

volume = 23.86in³

surface area = 16π in²

Explanation:

Given the diameter of the base of the cone = 4.0inches

radius of the cone = 4.0/2 = 2.0inches

slant height l = 6.0inches

Volume of the ice cream that made the cone = 1/3
`\pi r^(2)h`

to get the height of the cone we will use the Pythagoras theorem.

According to the theorem,
`hyp^(2)=Adj^(2)+opp^(2)`

given hyp = slant height = 6in

adjacent = base radius = 2in

height = opposite

opp =
`\sqrt{6^(2) - 2^(2) }`

opp =
`√(32)`

opp = height = 5.7in

Volume = 1/3 * 3.14 * 2² * 5.7

volume = 23.86in³

For the surface area;

Surface area of a cone = πr(r+l)

surface area = 2π(2+6)

surface area = 16π in²