Question : The heights of two cones are in the ratio 7 : 5 and their diameters are in the ratio 10 : 21. What is the ratio of their volumes? (Where $\pi=\frac{22}{7}$)
Option 1: 26 : 47
Option 2: 14 : 19
Option 3: 20 : 63
Option 4: 17 : 21
Correct Answer: 20 : 63
Solution : Ratio of heights, $h_1:h_2 =\frac{h_1}{h_2} = \frac{7}{5}$ Ratio of diameters, $d_1 : d_2 = \frac{d_1}{d_2} = \frac{10}{21}$ ⇒ Ratio of radii, $r_1 : r_2 = \frac{r_1}{r_2} = \frac{10}{21}$ Ratio of volumes of cones, $V_1 : V_2 = \frac{\frac{1}{3} \pi r_1^2 h_1}{\frac{1}{3} \pi r_2^2 h_2}= \frac{r_1^2 h_1}{r_2^2 h_2} = \frac{10^2 ×7}{21^2 × 5} = \frac{20}{63} = 20 :63$ Hence, the correct answer is 20 : 63.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : The heights of two right circular cones are in the ratio 1 : 5 and the perimeter of their bases are in the ratio 5 : 3. Find the ratio of their volumes.
Question : The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. The ratio of their volumes will be:
Question : The ratio of curved surface areas of two cones is 1 : 8 and the ratio of their slant heights is 1 : 4. What is the ratio of radii of the two cones?
Question : The volume of the two cones is in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. The ratio of their height is:
Question : The ratio of the volumes of two right circular cylinders A and B is $\frac{x}{y}$ and the ratio of their heights is a : b. What is the ratio of the radii of A and B?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile