Exercise 20F

### A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take π = 3.14]

Height of the cone (h) = 24 cm Height of the cylinder (H) = 36 cm Radius of the cone (r) = twice the radius of the cylinder = 10 cm Radius of the cylinder (R) = 5 cm \[\begin{array}{*{35}{l}}...

### A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is 4(2/3) m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.

Diameter of the base = 3.5 m So, its radius = 3.5/2 m = 1.75 m = 7/4 m Height of cylindrical part = 4 + 2/3 = 14/3 (i) \[\begin{array}{*{35}{l}} Capacity\text{ }\left( volume \right)\text{ }of\text{...

### A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.

Diameter of cylindrical boiler = 3.5 m So, the radius (r) = 3.5/2 = 35/20 = 7/4 m Height (h) = 2m Radius of hemisphere (R) = 7/4 m \[\begin{array}{*{35}{l}} Total\text{ }volume\text{ }of\text{...

### A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m; calculate: (i) total surface area of the tent (ii) area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching.

Height of the cylindrical part = H = 8 m Height of the conical part = h = (13 – 8) m = 5 m Diameter = 24 m Its radius \[\begin{array}{*{35}{l}} =\text{ }24/2\text{ }=\text{ }12\text{ }m  \\...

### A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 80 m, calculate the total area of canvas required. Also, find the total cost of canvas used at Rs 15 per meter if the width is 1.5 m

Radius of the cylindrical part of the tent (r) =105/2 m Slant height (l) = 80 m the total curved surface area of the tent \[\begin{array}{*{35}{l}} =\text{ }2\pi r\text{ }h\text{ }+\text{ }\pi rl ...

### From a solid cylinder whose height is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume and total surface area of the remaining solid.

Radius of solid cylinder (R) = 12 cm And, Height (H) = 16 cm \[\begin{array}{*{35}{l}} Volume\text{ }=\text{ }\pi {{R}^{2~}}h\text{ }=\text{ }22/7\text{ }x\text{ }12\text{ }x\text{ }12\text{...

### From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base are removed. Find the volume of the remaining solid.

Height of the cylinder (h) = 10 cm And radius of the base (r) = 6 cm Volume of the cylinder = πr2 h Height of the cone = 10 cm Radius of the base of cone = 6 cm \[\begin{array}{*{35}{l}}...