Question

See the picture below

Answer 1

a) 301.59 cubic centimeters

b) 235.87 square centimeters

Explanation:

a)

Volume of ice cream cone is volume of hemisphere PLUS volume of cone.

Volume of Hemisphere =
`((4)/(3)\pi r^3)/(2)`

radius is given as 4, so,

Volume of Hemisphere =
`((4)/(3)\pi r^3)/(2)\\=((4)/(3)\pi (4)^3)/(2)\\=134.04`

Now, Volume of Cone =
`(1)/(3)\pi r^2 h`

Where radius is 4 and height is 10, so,

Volume of Cone =
`(1)/(3)\pi r^2 h\\=(1)/(3)\pi (4)^2 (10)\\=167.55`

Volume of Ice Cream Cone = 134.04 + 167.55 = 301.59 cubic centimeters

b)

Surface area of ice cream cone is surface area of hemisphere PLUS surface area of cone.

Surface Area of Hemisphere =
`2\pi r^2\\=2\pi (4)^2\\=100.53`

Surface Area of Cone =
`\pi r^2+\pi rl`

We dont need to use the first part,
`\pi r^2` since it is "inside". We need to find l, slant height, by using pythagorean theorem on a triangle we can make (bottom right).

4^2 + 10^ 2 = l^2

16 + 100 = l^2

116 = l^2

l = 10.77

Now to find the surface area of cone =
`\pi rl\\=\pi (4)(10.77)\\=135.34`

Surface area of ice cream cone = 100.53 + 135.34 = 235.87 square centimeters