Question #fb4b5

1 Answer
Feb 27, 2016

Answer:

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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