Areas & Volumes — practice questions, page 3
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Two triangles are similar and the ratio of their perimeters is 3 : 5. If the area of the smaller…In triangle ABC, the point D lies on AB and E lies on AC so that DE is parallel to BC and AD : DB…The surface areas of two spheres are in the ratio 9 : 16. Find the ratio of their volumes.Two cones are similar in shape and the ratio of their volumes is 27 : 64. Find the ratio of their…The radius of a cylinder is doubled while its height is halved. Find the ratio of the new volume…The floor of a hall 20 m long and 15 m wide is to be carpeted at ₹250 per m², and a decorative…A rectangular field measures 50 m by 30 m. It is fenced all around at ₹40 per metre and levelled…A water tank open at the top is 5 m long, 4 m wide and 3 m deep. Find the area of sheet metal…A cylindrical vessel open at the top has radius 7 cm and height 10 cm. Find the area of metal in…From each corner of a square sheet of side 20 cm, a square of side 4 cm is cut off, and the four…A hollow metal pipe is 21 cm long. Its outer diameter is 10 cm and its inner diameter is 6 cm.…A cylindrical tube open at both ends is 20 cm long. Its outer radius is 9 cm and its inner radius…Water flows through a pipe of internal diameter 7 cm at a speed of 4 metres per second into an…Water flows at 15 km per hour through a pipe of internal diameter 14 cm into a rectangular tank…A cylindrical tank of radius 1.4 m and height 2.1 m is filled by a pipe of internal diameter 7 cm…Rain falls to a depth of 2 cm on a flat roof measuring 22 m by 20 m, and all of the water is…The largest possible sphere is carved out of a solid wooden cube of edge 21 cm. Find the volume of…A cone of the largest possible size is carved out of a solid cylinder of radius 7 cm and height 9…The sum of the length, breadth and height of a cuboid is 19 cm and the length of its space…The dimensions of a cuboid are in the ratio 2 : 3 : 6 and its volume is 288 cm³. Find the length…The areas of three adjacent faces of a cuboid are 15 cm², 20 cm² and 12 cm². Find its volume in cm³.A toy is a cone mounted on a hemisphere, both of radius 3.5 cm. The total height of the toy is…A solid is a cylinder of radius 7 cm with a hemisphere of the same radius fixed at each end. The…A model rocket is a cone standing on a cylinder, both of radius 7 cm. The cylinder is 20 cm high…A hemispherical hollow of the largest possible diameter is scooped out of one face of a solid…
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