Question
A cone and a hemisphere have the same base radius and
the same height. If the total volume of both is 2,160 cm³, find the radius.Solution
Volume of cone = (1/3)πr²h Volume of hemisphere = (2/3)πr³ Total volume = (1/3)πr²h + (2/3)πr³ = 2160 Since base radius and height are the same, let h = r. (1/3)πr³ + (2/3)πr³ = 2160 (1/3 + 2/3)πr³ = 2160 πr³ = 2160 r³ = 2160 / π = 2160 / 3.14 ≈ 687.58 r ≈ 8.8 cm Correct Option: a) 8.8 cm
- Manisha distributed 240 pencils among her three classmates—Nikhil, Arjun, and Sneha—in the ratio 2:3:5 respectively. Find the difference between the nu...
The speed of the boat A and B in still water are in the ratio 15:13. The speed of the current for both boats is 16 km/hr. If the sum of time taken by bo...
The ratio of the speed of the stream to the speed of the boat in still water is 3:7. If a distance of 280 km is covered downstream in 4 hours, determine...
The ratio of the monthly incomes of A and B is 11: 13 and the ratio of their expenditures is 9: 11. If both of them manage to save ₹4,000 per month, t...
- A piggy bank holds 20-paise, 50-paise and 2-rupee coins in the ratio 15:12:9. The total amount inside is Rs. 3006. How many 50-paise coins are there?
- If m : n = 2 : 3, then calculate the ratio (4m + n) : (m + 4n)
Ratio of present ages of mother and her son is 24:8 respectively. Father’s present age is 14 years more than that of mother. If the present average ag...
In a wallet, the proportion of one-rupee coins to two-rupee coins is 5:6. Within one section of the wallet, the ratio of one-rupee to two-rupee coins is...
A starts a business with Rs. 6600. After 3 months, B joins with A as his partner. After one year the profit is divided in the ratio 4:5. What is B&r...
