A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.
A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
Write ‘True’ or ‘False’ and justify your answer.
An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder
The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of water. The water pressure at the bottom of the trench is about 1.1 × 10⁸ Pa. A steel ball of initial volume 0.32 m³ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?
Write ‘True’ or ‘False’ and justify your answer.
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ballis 4/3 πa3
Write ‘True’ or ‘False’ and justify your answer.
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is 4πrh + 4πr2.
Write ‘True’ or ‘False’ and justify your answer.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 10⁷Pa? Assume that each rivet is to carry one quarter of the load.
Write ‘True’ or ‘False’ and justify your answer
Actual capacity of a vessel as shown in the Figure is equal to the difference of volume of the cylinder and volume of the hemisphere.
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