Question #fb4b5

1 Answer
SCooke · EZ as pi
Feb 27, 2016

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

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