About the volume

Question

A cone has a volume of 562.5pi cm^3. The radius of the base of the cone is equal to twice the height of the cone. Work out the curved surface area of the cone. Give answer to 3 sig figs.

Answer 1

V=(1/3)∏r²h

562.5∏=(1/3)∏r²h

562.5=(1/3)r²h

1687.5=r²h

h=height

radius=2h (radius is twice the height)

1687.5=(2h)²h

1687.5=4h³

h³=1687.5/4

h³=421.875

take the cube root of 421.875

h=7.5 cm

r=15 cm

use the Pythagorean Theorem to find the slant height, l

(7.5)²+(15)²=l²

56.25+225=l²

281.25=l²

l=√281.25

l=16.77 cm, or realize that l²=h²+(2h)², l²=5h², l=√5h, l=2.236*7.5=16.77 again

lateral surface area=∏*r*l

LSA=3.14159*15*16.77

LAS=3.14159*251.55

LAS=790.267 cm²