Height of cone = 8 cm Radius = 5 cm \[\begin{array}{*{35}{l}} Volume\text{ }=~1/3\text{ }\pi {{r}^{2~}}h \\ =\text{ }1/3\text{ x }22/7\text{ x }5\text{ x }5\text{ x }8\text{ }c{{m}^{3}} \\ =\text{...

### The cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.

Since, the diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm. radius = r = 7/2 cm It’s curved surface area = 2 πr2 = 2 x 22/7 x 7/2 x 7/2 = 77...

### 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:(iii) the weight of the material drilled out if it weighs 7 gm per cm3.

\[\left( iii \right)\text{ }Weight\text{ }of\text{ }material\text{ }drilled\text{ }out\text{ }=\text{ }1232\text{ x }7g\text{ }=\text{ }8624g\text{ }=\text{ }8.624\text{ }kg\]

### 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 the remaining solid (ii)the volume of remaining solid

Dimensions of rectangular solid l = 42 cm, b = 30 cm and h = 20 cm Conical cavity’s diameter = 14 cm its radius = 7 cm Depth (height) = 24 cm (i) Total surface area of cuboid...

### A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 m and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.

Radius of the hemisphere part (r) = 3.5 m = 7/2 m Volume of hemisphere \[\begin{array}{*{35}{l}} =\text{ }2/3\text{ }\pi {{r}^{3}} \\ =\text{ }2/3\text{ x }22/7\text{ x }7/2x\text{ }7/2\text{ x...

### 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.

Height of the cone = 15 cm Diameter of the cone = 7 cm its radius = 3.5 cm Radius of the hemisphere = 3.5 cm Volume of the solid = Volume of the cone + Volume of the hemisphere...