Question

Question #fb4b5

Answer 1

Yes, you use the formula for a cone volume to find the capacity.

depth = `sqrt147 ~~12.1cm`

capacity `~~622 cm^3`

Explanation:

`C = 2*pi*r " and "V = 1/3 * pi * r_2^2* h`

Diameter`= 28 cm , rarr r_1 = 14cm`

From the semicircular piece of metal we first find the circumference of the base of the cone, which is the same as ½ of the full circle,
`C = (2 * pi * r_1)/2`
`C = (2 * pi * 14)/2 = 14pi ~~ 44cm`

Now find our cone radius from the cone circumference.

`C = 2 * pi * r_2 rarr" " r_2 = (C/(2*pi))`

`r_2 = ( 14 pi)/(2*pi) = 7`

From Pythagoras, the equation for a right triangle

`r_1^2 = r_2^2 + h^2` we obtain:

`h = sqrt(r_1^2 – r_2^2) " "rarr" " h = sqrt(196 – 49)`

`h= sqrt 147( ~~ 12.1 cm" "` this is the depth of the cone cup)

`V = 1/3 * pi * r_2^2 * h`

`V = 1/3 * pi * 49 * sqrt147`

`V= 622 cm^3` volume capacity