Mensuration
Cylinder, Cone, Sphere and Hemisphere
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1. How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m in diameter?
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2. A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm³ of the metal weights 7.7 g.
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3. Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.
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4. Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitching. Also, find the cost of the canvas at the rate of Rs. 24 per meter.
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5. How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm ?
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6. A surahi is the combination of
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7. A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8 cm. The height of the cone is
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8. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
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9. An ice-cream cone full of ice-cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice-cream, provided that its 1/6 part is left unfilled with ice-cream.
2 points
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10. Water flows at the rate of 10 m min-1 through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
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