Q. 174.7( 10 Votes )
A tent is of the shape of a right circular cylinder up to a height of 3 m and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs 2 per square metre, if the radius of the base is 14 m.
Given: Height of cylinder “h” = 3 m
Radius “r” = 14 m
Height of tent “H” = 13.5 m
Cost of painting = Rs 2 per m2
Curved surface area of cylinder = 2πrh
Curved surface area of cone = πrl
We have, r = 14 m
h = 3 m
CSA of cylinder = 2πrh
= 264 m2
The height of the cone = Height of tent – height of cylinder
= 13.5 – 3
= 10.5 m
Now slant height of the cone is
Where r = 14 m and h = 10.5 m
We have shown, how to take square-root
⇒ l = 17.5 m
So CSA of cone = π r l
= 770 m2
Total area to be painted = CSA of the cylinder + CSA of the cone
= 264 m2 + 770 m2
= 1034 m2
Cost of painting 1 m2 = Rs 2
Cost of painting 1034 m2 = Rs 2 × 1034
= Rs 2068
Hence cost of painting the tent is Rs 2068.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
PREVIOUSA cylindrical pipe has inner diameter of 7 cm and water flows through it at the rate of 192.5 litres per minute. Find the rate of flow in kilometres per hour.NEXTTwo cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
RELATED QUESTIONS :
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. .RD Sharma - Mathematics
A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is . Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of ` 10 per cm2.RD Sharma - Mathematics
In Fig. 16.57, from a cuboidal solid metallic block, of dimensions 15 cm × 10 cm × 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block.
RD Sharma - Mathematics
A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy.RD Sharma - Mathematics
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.RD Sharma - Mathematics
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.RD Sharma - Mathematics
If the total surface area of a solid hemisphere is 462 cm2, find its volume.RD Sharma - Mathematics
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied out on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.RD Sharma - Mathematics
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed .RD Sharma - Mathematics