Areas & Volumes — practice questions, page 6
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QuestionA rectangle is drawn inside a semicircle of radius 5 cm with one of its sides lying along the…QuestionA triangle has a base 18 cm long and the height drawn to that base is 9 cm. A square is drawn…QuestionA regular hexagon has each side 14 cm. A circle is drawn through all six of its corners. Find the…QuestionA circle is drawn inside a regular hexagon of side 14 cm so that it touches all six sides. Find…QuestionAn equilateral triangle has side 12 cm. A circle is drawn inside it touching all three sides. Find…QuestionA square has side 20 cm. One circle is drawn through its four corners and a second circle is drawn…QuestionA car has two windscreen wipers whose swept regions do not overlap. Each wiper has a blade 21 cm…QuestionA wiper arm turns about a fixed pivot through an angle of 90°. The rubber blade does not reach the…QuestionA goat is tied by a 14 m rope to a corner peg of a square shed of side 7 m standing in an open…QuestionA goat is tied by a 7 m rope to a corner peg of a shed whose base is an equilateral triangle of…QuestionA corner is sawn off a cuboidal wooden block with one straight cut. The piece removed is a pyramid…QuestionA concrete loading ramp is a solid prism 9 m long. Its cross-section is a right-angled triangle…QuestionA swimming pool is 25 m long and 10 m wide. Its floor is flat but slopes evenly along the length,…QuestionAn open water channel is made from a pipe cut in half along its length, so its cross-section is a…QuestionAn open irrigation channel is 30 m long. Its cross-section is a trapezium 2 m wide across the top,…QuestionAn open channel is a half-pipe: a semicircular trough of internal radius 21 cm and length 10 m,…QuestionA metal ball of radius 6 cm has a hollow spherical cavity of radius 3 cm at its centre. Find the…QuestionA hollow metal sphere has external radius 10 cm and the metal is 3 cm thick everywhere. Find the…QuestionA solid cone is cut by a plane parallel to its base passing through the midpoint of its axis, so…QuestionA solid cone has base radius 14 cm and vertical height 12 cm. A plane parallel to the base cuts it…QuestionA solid cone is cut by a plane parallel to its base so that the small cone removed has one-third…QuestionA cone has base radius 15 cm and vertical height 20 cm. A plane parallel to the base cuts off the…QuestionA cubical block of wood of edge 10 cm and mass 600 g floats in water. A floating body sinks until…QuestionAn iceberg floats with exactly one-ninth of its volume above the water surface. The part standing…QuestionA garden roller is a cylinder 1.4 m long whose diameter is 0.7 m. Find the area of ground it…
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