Question
A solid right circular cone of radius 8 cm and height 4 cm is melted and recast into a solid sphere. What is the radius of the sphere (in cm)?
Solution
ATQ, Volume of cone = (1/3)πr²h = (1/3)π × 8² × 4 = (1/3)π × 64 × 4 = (256/3)π. Volume of sphere = (4/3)πR³. Equate: (4/3)πR³ = (256/3)π ⇒ 4R³ = 256 ⇒ R³ = 64 ⇒ R = 4 cm.
More Mensuration Questions
- The length is increased by 25%, breadth remains unchanged, and the height is reduced by 20%. Find the net percentage change in volume.
- If a six digit number 3x 7z 8y is divisible by 7, 11, 13, then the average value of x, y, z is:
- AB is the diameter of a circle with center o. P is the point on it If the cone ∠AOP is equal to 98 degrees then ∠OBP will be.
- Inside a square land having perimeter equal to 76 metres, leaving aside a circular land of radius 7 metres, the remaining land needs to be levelled at a co...
- The radius and height of a right circular cone are in the ratio 3: 4. If its curved surface area (in cm²) is 240 π, then its volume (in cm&su...
- Question 6
- The circumference of a square and the circumference of a cube are equal. The numerical value of the total surface area of the cube is 25 times the perimete...
- A race track is in the shape of a rectangle with length of 75 metres and area of 3000 m2. A car takes 20 seconds to make one lap around the perimeter of th...
- The length is decreased by 18%, the breadth is decreased by 12% and the height is increased by 50%. Calculate the percentage change in the volume of the cu...
- The length of a rectangle is 15 m and its breadth is 10 m. What is its area?
