From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm
and depth 24 cm is drilled out. Find:
(i) the surface area of remaining solid,
(ii) the volume of remaining solid
(iii) the weight of the material drilled out if it weighs 7 gm per `cm^3`.
A vessel is in the form of an inverted cone its height is 8 cm and the radius of its top, which is open, is 5 cm. If is filled with water up to the rim. When lead shots each of which is a sphere of radius 0.5 cm are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots sopped in the vessel.
The area of the base of a conical solid is 38.5 cm2 and its volume is 154 cm3. Find curved surface area of the solid.
A solid metallic cone, with radius 6 cm and height 10cm, is made of some heavy metal A. In order to reduce its weight, a conical hole is made in the cone as shown and it is completely filled with a lighter metal B. The conical hole has a diameter of cm and depth 4 cm calculate the ratio of the volume of metal A to the volume of the metal B in the solid.
The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.
A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed.
A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.