Question

the volume V of a cone is 200 cm^3 . another cone has a height 6 times bigger with a base radius half as long. what is the volume of this cone?

Answer 1

v=1/3$\pi$r²h
200=1/3$\pi$r²h
600=$\pi$r²h
vol. of 2nd cone
v=1/3$\pi$(r/2)²6h
v=1/2$\pi$r²h
putting the value of tex] \pi [/tex]r²h=600
v=1/2*600
vol. of 2nd cone=300cm³

Answer 2

$v = \frac{1}{3} \pi {r}^{2} h = 200 {cm}^{3} \\ if \: h 1= 6h \\ r1 = \frac{1}{2} r \\ volume = \frac{1}{3} \pi {( \frac{r}{2} )}^{2} 6h \\ = \frac{1}{3} \pi {r}^{2} h \times \frac{6}{4} = 200 \times \frac{6}{4} = 50 \times 6 = 300 {cm}^{3}$