Areas & Volumes — practice questions, page 11
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QuestionThe largest possible sphere is carved out of a solid cylinder of radius 3 cm and height 10 cm.…QuestionA hemispherical bowl holds 2.4255 litres of water when filled level to the brim. Find its internal…QuestionA steel bar is a prism 20 cm long whose cross-section is a regular hexagon of side 6 cm. Find its…QuestionA solid glass paperweight is a cone of volume 1232 cm³ standing on a base of diameter 14 cm. Find…QuestionA rectangular pit 6 m long and 4 m wide is lined with cement on its floor and on its four vertical…QuestionA solid brass cone has base radius 7 cm and weighs 5.39 kg. Brass weighs 7 g per cm³. Find the…QuestionThe diagonal drawn across ONE FACE of a cube measures 10 cm. Find the total surface area of the…QuestionA medicine capsule is a cylinder with a hemisphere closing each end, and every part has radius 3…QuestionA solid cube of edge 6 cm and a solid sphere have exactly the same surface area. Which of the two…QuestionA grain hopper is an upside-down pyramid: its open top is a square of side 6 m and it narrows to a…QuestionA closed cylindrical tin has radius 7 cm and its total surface area is 968 cm². Find its height in…QuestionHow many solid cubes of edge 6 cm can be packed inside an open box measuring 25 cm by 20 cm by 15…QuestionFour identical balls are stacked one above another inside a closed cylindrical tin. Each ball…QuestionA hemispherical metal bowl has internal radius 5 cm and the metal is 1 cm thick everywhere. Find…QuestionThe curved surface area of a cone is 550 cm² and its base radius is 7 cm. Find its vertical height…QuestionAn oval running track has two straight sides joined by two semicircular ends. Two runners start…QuestionA verandah is held up by identical cylindrical pillars, each 3.5 m tall and 0.4 m in diameter.…QuestionA cylindrical drum of internal radius 21 cm and internal height 50 cm is filled to the brim from a…QuestionA cylindrical tin has internal radius 6 cm and internal height 16 cm. Find the length of the…QuestionA pile of gravel at a building site is a cone whose base circumference is 88 m and whose slant…QuestionThe four walls of a rectangular room have a combined area of 120 m², and the room is 4 m high.…QuestionTwo solid cubes of edge 4 cm are glued together face to face to form a single cuboid. Find the…QuestionA cylinder has curved surface area 1320 cm² and the circumference of its base is 44 cm. Find its…QuestionThe edge of a cube is measured 2% too long. By what percent will the volume calculated from that…QuestionThe base radius and the vertical height of a cone are in the ratio 3 : 4, and its volume is 301.44…
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