Question

Can someone help me solve for surface area and volume?

Answer 1

`color(maroon)("Surface Area " = 350 pi " in"^2`

`color(blue)("Volume " = (500 * (sqrt 5 + 4))/3pi " in"^3`

Explanation:

To find Surface Area and Volume of the given figure.

1. Surface Area `A_s` = surface Area of Cone + Surface Area of Hemisphere.

`A_s = pi r l + 2 pi r^2 = (pi * 10 * 15 + (2 * pi * 10^2)`

`A_s = 150 pi + 200 pi = 350 pi " in"^3`

1. Volume = V = Volume of Cone + Volume of hemisphere.

`V = (1/3) pi r^2 h + (2/3) pi r^3`

`h = sqrt(15^2 - 10^2) = 5 sqrt5 " in"`

`V = (1/3) pi * 10^2 * 5sqrt5 + (2/3) pi * 10^3 " in"^3`

`V =(500 sqrt 5 pi + 2000 pi)/3 " in"^3`

`V = (500 * (sqrt 5 + 4))/3pi " in"^3`

Answer 2

`"Volume" =(500(sqrt5 +4)pi)/3` cubic inches

`SA = 350pi` squ inches

Explanation:

This question can be answered by the applying the correct formulae and substituting the given values.

`"Volume = volume of cone + volume of hemisphere"`

`V = color(blue)((pir^2h)/3) + color(red)((4pir^3)/3 div2)`

Find the height of the cone using Pythagoras' Theorem.

`h^2 = 15^2 -10^2`

`h = sqrt125`

`V =color(blue)((pi (10^2)(sqrt125))/3) + color(red)((2 pi (10^3))/3)`

`V = ((10^2)(sqrt125)pi + 2(10^3)pi)/3`

`V=((10^2)pi(5sqrt5+20))/3`

`V=((10^2)pi(5sqrt5+20))/3`

`V=(5xx100(sqrt5 +4)pi)/3`

`V=(500(sqrt5 +4)pi)/3` cubic inches

`"Surface area = curved surface of cone + curved surface of hemisphere"`

`TSA = pi r l + 4pir^2 div2`

`TSA = pi(10)(15)+ 2pi(10^2)`

`TSA = 150pi +200pi`

`TSA = 350pi` squ inches