Advertisements
Advertisements
Question
A cylindrical pillar has a radius of 21 cm and a height of 4 m. Find:
- The curved surface area of the pillar.
- cost of polishing 36 such cylindrical pillars at the rate of ₹12 per m2.
Advertisements
Solution
r = 21 cm, h = 4 m = 400 cm
i. C.S.A = 2πrh
= `2 xx 22/7 xx 21 xx 400`
= 52800 cm2
= `52800/(100 xx 100) = 5.28` m2
ii. Rate = ₹12/m2
Area to be polished = (5.28 × 36) m2
Cost = 12 × Area
= 12 × 5.28 × 36
= ₹2280.96
APPEARS IN
RELATED QUESTIONS
The floor of a rectangular hall has a perimeter 250 m. If the cost of panting the four walls at the rate of Rs.10 per m2 is Rs.15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area.]
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
Hameed has built a cubical water tank with lid for his house, with each other edge 1 .5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of tiles is Rs. 360 per dozen.
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm in following figure. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2. Find the total expenses required for polishing and painting the surface of the bookshelf.
A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide, find its height.
What will happen to the volume of a cuboid if its Length is doubled, height is doubled and breadth is sama?
Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm.
Find the surface area of a cuboid whoselength = 3.2 m, breadth = 30 dm, height = 250 cm.
The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2 = xyz.
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its dimensions.
The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square metre is Rs 340.20 and the cost of matting the floor at 85 paise per square metre is Rs 91.80. Find the height of the room.
Find the edge of a cube whose surface area is 432 m2.
If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.
If each edge of a cube is increased by 50%, the percentage increase in its surface area is
A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is
The dimensions of a Cinema Hall are 100 m, 60 m, and 15 m. How many persons can sit in the hall if each requires 150 m3 of air?
A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.
The external dimensions of a closed wooden box are 27 cm, 19 cm, and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:
- The volume of the wood in the box;
- The cost of the box, if wood costs Rs. 1.20 per cm3;
- A number of 4 cm cubes that could be placed into the box.
A solid cube of edge 14 cm is melted down and recast into smaller and equal cubes each of the edge 2 cm; find the number of smaller cubes obtained.
The dining-hall of a hotel is 75 m long; 60 m broad and 16 m high. It has five – doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of Rs.12 per m2;
(ii) carpetting its floor at the rate of Rs.25 per m2.
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) the total surface area of the cuboid.
(iii) the total surface area of the cube.
(iv) which of these two has a greater surface and by how much?
Find the capacity of a cylindrical container with an internal diameter of 28 cm and a height of 20 cm.
If the edge of a cube is 8 cm long, find its total surface area.
Find the volume of a cuboid whose diagonal is `3sqrt(29)"cm"` when its length, breadth and height are in the ratio 2 : 3 : 4.
The length of a cold storage is double its breadth. Its height is 3m. The area of its four walls including doors is 108m2. Find its volume.
External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm2 is Rs 11,750, find the dimensions of the box.
