Maths Question

A right circular cone has a base radius of 3r cm, a height of h cm and a volume of 90 cm３. For a cylinder of base radius 3r cm and height 3h cm, its volume is?

Volume of circular cone =1/3 area of the base*height
90cm3=1/3 π (3r)2*h
90=1/3 (9r2π h)
30=π r2h --(1)

Volume of cylinder=area of the base*height
Volume of cylinder= π (3r)2*3h
Volume of cylinder= 9r2π *3h
Volume of cylinder=27π r2h **from (1) ,we know that π r2h=30cm3**
Volume of cylinder=27(30)
Volume of cylinder=810cm3





2007-01-03 18:59:14 補充：
樓上個兩位都有式錯左= ="

The equation of finding volume of a right circular cone is
V=1/3πr^2h,where V is volume,r is base radius,h is the height.

since the right circular cone has a base radius of 3r cm, a height of h cm and a volume of 90 cm^3,to find the volume cylinder of base radius 3r cm and height 3h cm,we know that the only difference between two cone is the height where one is h,one is 3h,which is 1:3.Hence,the volume of these two cone is also 1:3


Hence,the volume of the required cone is (3 x 90)cm^3=270cm^3

2007-01-03 19:07:12 補充：
Sorry,i made a big mistake that the required answer is not for a cone but a cylinder.so,the volume of the required answer is (3 x 3 x 90)cm^3=810cm^3

Volume of a cone = (1/3)(π)(r)^2(h),
where r is the base radius of the cone, h is height of the cone, π = 3.14

90 = (1/3)(π)(3r)^2(h)
90/h = (1/3)(π)(3r)^2

The required volume
= (1/3)(π)(3r)^2(3h)
= 90/h (3h)
= 270 cm3