Question Bank
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Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume of the solid.
A circus tent is cylindrical to a height of 3 m and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, find the total volume of air inside.
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Find the number of cones.
The ratio of the volumes of two cones is 1:4 and their diameters are in the ratio 4:5. Find the ratio of their heights.
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones.
A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. Find the volume of water it can hold.
A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs 10 per m²? (Wait, volume question requested). Find the volume of the tank.
A cylindrical pipe has inner diameter 4 cm and water flows through it at 20 m/min. How long would it take to fill a conical vessel of radius 40 cm and depth 72 cm?
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Find the volume of the remaining solid.
The rain water from a roof of 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the vessel is just full, find the rainfall in cm.
Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. If the radius of the cylinder is 60 cm and its height is 180 cm, find the volume of water left in the cylinder.
If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?
What is the volume of a sphere whose surface area is 36π cm²?
Find the volume of a right circular cylinder with height 20 cm and radius 7 cm.
A cuboid of volume 96 cm³ has a length of 8 cm and a breadth of 3 cm. Find its height.
A pyramid has a volume of 100 cm³. If its height is 12 cm, find the area of its base.