Question

Find the height of a prism with a base in the form of a sector in which the central angle is 25 degree . its volume is found to be 350 in^3. and the height is four times the radius of the base.

Answer 1

V=BH

`B=A_(sector)= (r^2\pi\alpha)/(360^o) \\H=4r \\350= (r^2\pi* 25^o)/(360^o)4r \\350= (r^3\pi* 100^o)/(360^o) \\ r^3* 3.14* 100^o=350* 360^o \\r^3= (350* 360^o)/(3.14* 100^o) \\r= \sqrt[3]{(350* 360^o)/(3.14* 100^o) } \\H=4r=4 \sqrt[3]{(350* 360^o)/(3.14* 100^o) } \approx 29.5`