Mensuration I

A vessel in the form of an inverted cone is filled with water to the brim. Its height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows. What is the volume of each of the solid cone submerged? (2002)

Given height of the cone, h = 20 cm Diameter of the cone = 16.8 cm Radius of the cone, r = 16.8/2 = 8.4 cm Volume of water in the vessel = (1/3)r2h = (1/3)×8.42 ×20 = (1/3)×(22/7)×8.4 ×8.4 ×20 =...

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A bucket is ascended by a rope from well which is wound round a wheel having diameter of 35 cm. If the bucket is ascended from well with a uniform speed of 1.1 m/sec in 2 minutes , calculate the number of full revolutions the wheel makes while raising the bucket.

According to given question, Diameter of wheel, $d=35cm$ Radius of circle = Half of the diameter $r=d/2$ So, Radius of wheel $=35/2=17.5cm$ Circumference of circle $=2\pi r$ $=2\times 22/7\times...

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