If the radius of a cone decreases by 20% when its height is increased by 50%, then what will be the percentage change in its volume?
4% decrease
Volume of cone = (1/3)πr²h, so the volume varies as r² × h.
New radius = 0.8r (20% decrease)
New height = 1.5h (50% increase)
New volume factor = (0.8)² × 1.5
= 0.64 × 1.5
= 0.96
Change = 0.96 - 1 = -0.04, i.e. 4% decrease
Hence, 4% decrease.
Similar Questions
A copper wire 36 m long with a diameter of 2 mm is melted to make a sphere. Then the radius of the sphere is ______.
The cost of paper is ₹55 per kilogram. If one kilogram of paper covers an area of 192 m2, then what will be the cost (in ₹) to cover a cube with an 8 metre edge?
When Jaya divided the surface area of a sphere by the volume of the sphere, she got the answer 2/3 cm. What is the radius of the sphere?
Shyam's room has dimensions 5 m × 3 m × 2 m. The room also has a door of dimensions 2 m × 1.5 m and a window of dimensions 1 m × 1 m. If the rate of painting is ₹1.50 per m², what will be the cost (in ₹) of painting the four walls of his room?
The base of a prism is an equilateral triangle with side 5 m, and its height is 20 m. The volume of the prism is:
How many cubes of side 5 cm can be placed in a cubical box of side 2 m?
The curved surface area of a right circular cone is 1000 cm² and its radius is 10 cm. What is its volume? (in cm³)
A cone and a hemisphere have equal bases and equal volumes. If the height of the cone is 12 cm, then what will be the radius of the hemisphere?
The radius of a metal sphere is 9 cm. It is melted and drawn into a wire of 0.3 cm, then what is the length of the wire (in m)?
The curved surface area of a cylinder is 1056 cm2. If the height of the cylinder is 8 cm, then what will be the diameter of its base?
Important Questions from 3-D Mensuration
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
The length and breadth of a cuboid are 50 cm and 75 cm, respectively. If the length of the diagonal is $17\sqrt{29}$ cm, then what is the volume (in $cm^{3}$) of the cuboid?
