Question
The radius of a sphere is 75% of the radius of a
cylinder, while the height of the cylinder is 25% greater than its radius. Determine the ratio of the volume of the sphere to that of the cylinder.Solution
Let the radius of the cylinder be '4a' units. So, the height of the cylinder = 4a X (5/4) = '5a' units Radius of the sphere = 4a X 0.75 = '3a' units Volume of the sphere = (4/3) X π X radius3 Volume of the cylinder = π X radius2 X height Therefore, required ratio = ((4/3) X π X radius3) :(π X radius2 X height) = [(4/3) X π X (3a) 3]:[π X (4a) 2 X 5a] = 36:80 = 9:20
There are five friends, P, Q, R, S and T. P says to Q, “If you give me Rs 300, you will have as many as I have at this moment. If S takes Rs 500 f...
A cuboidal box has dimensions of length = 18 cm, breadth = 15 cm, and height = 10 cm. If the breadth is increased by 20% and the height is decreased by ...
The average of x numbers is 24. If 60% of these numbers are reduced by 5 and the remaining 40% are increased by 10, what will be the new average of the ...
The difference between the interest earned from investing ₹P in simple interest at an annual rate of 25% and the interest earned from investing the sa...
Vinay invested Rs. 9,500 in scheme 'A' at a simple interest rate of 12% per annum and Rs. 8,000 in scheme 'B' at a simple interest rate of 20% per annum...
In a village with a population of 8,500 people, 80% of them are adults. Among these adults, only 75% possess a ration card. Furthermore, 60% of the rati...
Rakesh travels a certain distance with a constant speed of 24 km/h such that he reaches 2 hours late. If he travelled at constant speed of 30 km/h he wo...
Two pipes, A and B, can independently fill the tank in 24 minutes and 30 minutes respectively, while pipe C can empty 9 gallons from the tank in 3 minut...
Find the sum of first 25 even numbers.
A boat has a speed of 30 km/h in still water. In a particular stream, the boat's downstream speed is 50% faster than its speed upstream. What is the spe...
Relevant for Exams:
