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Areas & Volumes — practice questions, page 5

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A cylindrical vessel of radius 6 cm and height 15 cm is filled with water to the brim. A solid…A trophy is a solid built from three parts stacked on one vertical axis, all of radius 10.5 cm: a…A cylindrical container of radius 6 cm and height 15 cm is full of ice cream. The ice cream is…A metal rod of diameter 1 cm and length 8 cm is drawn out into a wire of uniform diameter 2 mm.…A solid metallic sphere of radius 9 cm is melted and drawn into a wire of uniform circular…A well of diameter 14 m is dug 10 m deep. The earth taken out is spread evenly all around the well…A well of diameter 7 m is dug 8 m deep, and the earth taken out is spread evenly over a…A solid prism has an equilateral triangle of side 8 cm as its base and is 15 cm long. Taking √3 =…The base of a right prism is a right-angled triangle whose two shorter sides are 6 cm and 8 cm,…A pyramid stands on a base that is a right-angled triangle with legs 9 cm and 12 cm, and the apex…A pyramid has an equilateral triangle of side 6 cm as its base and its vertical height is 10 cm.…A solid rectangular parallelepiped measures 25 cm by 15 cm by 10 cm. It is cut without waste into…A circular running track has an inner circumference of 352 m, and the track itself is 7 m wide all…A circular track is 3.5 m wide. By how many metres is one lap along its outer edge longer than one…Two circles of radii 21 cm and 14 cm share the same centre. Two radii drawn from that centre make…A flower bed is the region lying between two circles of radii 14 m and 7 m drawn about the same…One triangle has sides 6 cm, 8 cm and 10 cm. A second triangle has sides 15 cm, 20 cm and 25 cm.…A triangle has sides 7 cm, 24 cm and 25 cm. A second triangle is drawn with every side three times…A triangle has sides 26 cm, 28 cm and 30 cm. A second triangle is similar to it and has perimeter…Two cones are similar in shape, one being a scale model of the other. Their heights are 5 cm and 8…Two jugs are similar in shape and their heights are in the ratio 2 : 3. The smaller jug holds 240…Two solid statues are cast from the same metal and are similar in shape. Their heights are 30 cm…Two boxes are similar in shape, one being a scale model of the other, and the ratio of their…A square is drawn inside a semicircle of radius 10 cm so that one whole side of the square lies…A right-angled triangle has its two perpendicular sides 6 cm and 12 cm long. A square is drawn…

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