The radius of a cylinder is increased by 33 % and its height is decreased by x% such that the volume of the cylinder remains unchanged. Find x.
43.75
Volume of a cylinder V = πr²h. After change, new radius = 1.33 r, so new r² = (1.33)² r² = 1.7689 r².
For V to stay the same, new h × 1.7689 = old h, so new h = old h / 1.7689 ≈ 0.5625 × old h.
Reduction in h = 1 − 0.5625 = 0.4375, i.e. 43.75%.
Hence, the answer is 43.75.
Similar Questions
A cylinder whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. Find the number of spherical balls.
A room with a square base and height 10 ft occupies 25,000 ft3 volume. The room has cubicles of base area 25 ft2 in four corners. The walls and ceiling of the area of the room which is not occupied by cubicles is to be painted. How much area is to be painted?
In a parallelogram, the length of its two adjacent parallel sides are 11.9 cm and a cm where a is the smaller side. If the perpendicular distance between the two longer and shorter sides are 3.9 cm and 5.1 cm, find the perimeter of the parallelogram.
If the curved surface area of a cylinder of height 6 cm is 264 cm², then its volume is: (Use π = 22/7)
7600 bricks, each measuring P cm × 12.5 cm × 7.5 cm, are required to construct a wall 6 m long, 5 m high, and \(\frac{1}{2}\) m thick. If the cement and sand mixture occupies \(\frac{1}{20}\) of the volume of the wall, then the value of P is:
A regular hexagon is inscribed within a circle. If the area of the hexagon is \(144\sqrt{3}\) square units, determine the ratio of the circumference of the circle to the perimeter of the hexagon.
During a craft activity, a student creates a paper model in the shape of a right circular cone. The cone has a volume of 100π cm3 and a height of 12 cm. Find the curved surface area (in cm2) of the cone. Give your answer in terms of π.
Find the volume of a cone, whose slant height is 25 cm and curved surface area is 942 cm2 (rounded off to two places of decimal, use π = 3.14, and \(\sqrt{481} = 21.93\)).
The company has two options to pack a certain item.
Box A: Cubical box of side 5 cm
Box B: Cuboidal box of l = 6 cm, b = 4 cm and h = 3 cm.
The cost of cardboard required to make boxes is ₹10/cm2. However, box A uses 10% more cardboard while box B uses 15% more cardboard due to fold and turns.
Which box will the company prefer to minimise the total cost of cardboard and what is the cost of making it?
The surface area of a sphere is numerically equal to the volume of another sphere. If the radius of the first sphere is 7 cm, find the radius (in cm) of the second sphere.
Important Questions from Mensuration
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?
A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden
A village having a population of 4000 requires 150 liters of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for
The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is
