Question
In a right circular cone, the radius of its base is 7 cm and its height is 24 cm. A cross-section is made through the mid-point of the height parallel to the base. The volume of the upper portion is :
Answer: Option A $$\eqalign{
& r = 7{\text{ cm, }}h{\text{ = 24 cm}} \cr
& {\text{Now, }}\vartriangle {\text{AOB}} \sim \vartriangle {\text{COD}} \cr
& {\text{So, }}\frac{{OA}}{{OC}} = \frac{{AB}}{{CD}} \cr
& \Rightarrow \frac{h}{{\frac{h}{2}}} = \frac{r}{{CD}} \cr
& \Rightarrow CD = \frac{r}{2} \cr} $$
∴ Volume of upper portion :$$\eqalign{
& = \frac{1}{3}\pi {\left( {\frac{r}{2}} \right)^2}\left( {\frac{h}{2}} \right) \cr
& = \left( {\frac{1}{3} \times \frac{{22}}{7} \times \frac{7}{2} \times \frac{7}{2} \times 12} \right){\text{ c}}{{\text{m}}^3} \cr
& = 154{\text{ c}}{{\text{m}}^3} \cr} $$
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