Advertisements
Advertisements
प्रश्न
The ratio between the curved surface area and the total surface area of a cylinder is 1: 2. Find the ratio between the height and the radius of the cylinder.
Advertisements
उत्तर
Let r be the radius and h be the height of a right circular cylinder, then Curved surface area = 2πrh
and total surface area = 2πrh x 2πr2 = 2πr(h + r)
But their ratio is 1: 2
`therefore (2pirh)/(2pir(h + r)) = 1/2`
⇒ `h/(h + r) = 1/2`
⇒ 2h = h + r
⇒ 2h - h = r
⇒ h = r = 1 : 1
Hence, their radius and height are equal.
APPEARS IN
संबंधित प्रश्न
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?
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost
of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost ofcovering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m2 is Rs.1248. Find the dimensions of the box.
An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 m. Find the cost of painting the inner surface of Rs 50 per sq. metre.
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 volume of a cuboid whose length = 15 cm, breadth = 2.5 dm, height = 8 cm.
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
How many bricks each of size 25 cm × 10 cm × 8 cm will be required to build a wall 5 m long, 3 m high and 16 cm thick, assuming that the volume of sand and cement used in the construction is negligible?
The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?
A swimming pool is 20 m long 15 m wide and 3 m deep. Find the cost of repairing the floor and wall at the rate of Rs 25 per square metre.
A classroom is 7 m long, 6 m broad and 3.5 m high. Doors and windows occupy an area of 17 m2. What is the cost of white-washing the walls at the rate of Rs 1.50 per m2.
Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.
The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2 = xyz.
A field is 150 m long and 100 m wide. A plot (outside the field) 50 m long and 30 m wide is dug to a depth of 8 m and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?
The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 m3 of air?
The volume of a cube whose surface area is 96 cm2, is
Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is
Four cubes, each of edge 9 cm, are joined as shown below :
Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and the volume
The dimension of a class-room are; length = 15 m, breadth = 12 m and height = 7.5 m. Find, how many children can be accommodated in this class-room; assuming 3.6 m3 of air is needed for each child.
Find the area of metal-sheet required to make an open tank of length = 10 m, breadth = 7.5 m and depth = 3.8 m.
A closed box is made of wood 5 mm thick. The external length, breadth and height of the box are 21 cm, 13 cm and 11 cm respectively. Find the volume of the wood used in making the box.
A room is 5m long, 2m broad and 4m high. Calculate the number of persons it can accommodate if each person needs 0.16m3 of air.
Find the length of the largest pole that can be placed in a room of dimensions 12 m × 4 m × 3 m.
Below are the drawings of cross sections of two different pipes used to fill swimming pools. Figure A is a combination of 2 pipes each having a radius of 8 cm. Figure B is a pipe having a radius of 15 cm. If the force of the flow of water coming out of the pipes is the same in both the cases, which will fill the swimming pool faster?
