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
$B=A_{sector}= \frac{r^2\pi\alpha}{360^o} \\H=4r \\350= \frac{r^2\pi\times 25^o}{360^o}4r \\350= \frac{r^3\pi\times 100^o}{360^o} \\ r^3\times 3.14\times 100^o=350\times 360^o \\r^3= \frac{350\times 360^o}{3.14\times 100^o} \\r= \sqrt[3]{\frac{350\times 360^o}{3.14\times 100^o} } \\H=4r=4 \sqrt[3]{\frac{350\times 360^o}{3.14\times 100^o} } \approx 29.5$