किसी शंकु के आधार का क्षेत्रफल `770 cm^(2)` उसके तिर्यक पृष्ठ का क्षेत्रफल `814 cm^(2)` है। आयतन ज्ञात करें?
A. `213 sqrt(3)cm^(3)`
B. `392sqrt(5)cm^(3)`
C. `550sqrt(5)cm^(3)`
D. `616sqrt(5)cm^(3)`
A. `213 sqrt(3)cm^(3)`
B. `392sqrt(5)cm^(3)`
C. `550sqrt(5)cm^(3)`
D. `616sqrt(5)cm^(3)`
Correct Answer – D
`pir^(2)=770`
`impliesr^(2)=(770xx7)/22`
`implies r=7sqrt(5)cm` ltrbgt and `pirl=814`
`l=(814xx7)/(22xx7sqrt(5))=37/(sqrt(5))`
`l^(2)=h^(2)+r^(2)`
`=(37xx37)/4=h^(2)+245`
`impliesh^(2)=1369/5-245=144/5`
`implies h=12/(sqrt(5))`
volume `=1/3pir^(2)h`
`=1/3xx22/7xx7sqrt(5)xx7sqrt(5)xx12/(sqrt(5))`
`616sqrt(5)cm^(3)`