A float in a shape of a cone on top of a hemisphere is made from solid rubber. The diameter of the hemisphere is 30cm and the height of the float is 60cm.
(i) Find the volume of the float in term s of pi
The float is cut from a solid rubber cylinder of diameter 30cm and height 60cm.
(ii) Express the volume of rubber used in the float as a percentage of the volume of the cylinder. Give your answer to the nearest whole number.
+118658 A float in a shape of a cone on top of a hemisphere is made from solid rubber. The diameter of the hemisphere is 30cm and the height of the float is 60cm.
(i) Find the volume of the float in term s of pi
The float is cut from a solid rubber cylinder of diameter 30cm and height 60cm.
radius=15cm height of cone=45cm
\(Volume=\frac{4}{3}\pi r^3+\frac{1}{3}\pi r^2h\\ Volume=\frac{4}{3}\pi *15^3+\frac{1}{3}\pi *15^2*45\\ Volume=\frac{15^2\pi}{3}*4 *15+\frac{15^2\pi}{3} *45\\ Volume=15^2\pi*4 *5+15^2\pi*15\\ Volume=15^2\pi(4 *5+15)\\ Volume=225\pi(35)\\ Volume=7874\pi \;\;cm^3\\ Volume=7.874\pi \;\;Litres \)
(ii) Express the volume of rubber used in the float as a percentage of the volume of the cylinder. Give your answer to the nearest whole number.
\(Volume\;of\;cylinder=\pi *15^2*60\\ Volume\;of\;cylinder=\pi *225*60\\~\\ \mbox{Volume of float as a percentage of Cylinder}\\ =\frac{225*35*\pi}{225*60*\pi}*\frac{100}{1}\%\\ =\frac{350}{6}\%\\ =55.8\dot{3}\%\\ \approx 56 \%\)
