Question

a small cone is cut of from the top by a plane parallel to its base passing through the middle point .if the radius of the whole cone is 14 cm .compare the volume of the 2 parts of cone​

Answer 1

Hey mate !

_________________

Let DO' = r cm and OO'= h cm.

As ∆ADO' and ∆ABO are similar

\therefore {\mathsf{\frac{AO'}{AO} = \frac{DO'}{BO}}}

\mathsf{ \implies \frac{9 - h}{h} = \frac{r}{3} } \\ \\ \mathsf{ \implies 9 - h = 3r} \\ \\ \mathsf{ \implies h = 9 - 3r}

Volume of Frustum

\mathsf{ \implies \frac{1}{3}\pi h \: (r {}^{2} \: _1 + r {}^{2} \: _2 +r _1r _2) } \\ \\ \mathsf{ \implies 44 = \frac{1}{3} \times \frac{22}{7} \times (9 - 3r)(3 {}^{2} + 3r + r {}^{2} ) } \\ \\ \mathsf{ \implies \frac{44 \times 7}{22} = 3 { }^{3} - r {}^{3} } \\ \\ \mathsf{ \implies 14 = 27 - r {}^{3} } \\ \\ \mathsf{ \implies r {}^{3} = 27 - 14 } \\ \\ \mathsf{ \implies r {}^{3} = 13 } \\ \\ \mathsf{ \implies r = \sqrt[3]{13} } \\ \\ \bold{hence} \\ \\ \mathsf{ \therefore r = \sqrt[3]{13} }