Advertisements
Advertisements
प्रश्न
The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find, its diameter and its length.
Advertisements
उत्तर
Let the radius of a toy = r and
height of the toy = h
The curved surface area of a toy = 132 cm2
=> 2πrh = 132 cm2
⇒ `2pirh = 132` cm2
⇒ `r = 132/(2pi xx h)` cm2 ...(i)
Also, volume of a toy = 462 cm3
⇒ `pir^2h = 462` cm3
⇒ `r^2 = 462/(pi xx h)` ...(ii)
Now, substitute the volume of r, we get
`(132)^2/((2)^2 xx (pi)^2 xx h^2) = 462/(pi xx h)`
⇒ `132^2/(4 xx pi xx h) = 462`
⇒ `4 xx pi xx h = (132 xx 132)/462`
⇒ `h = (132 xx 132)/(462 xx pi xx h)`
⇒ `h = (132 xx 132 xx 7)/(462 xx 22 xx 4) = 3` cm
Now, put the value of h in eq. (i), we get
`r = (132 xx 7)/(2 xx 22 xx 3) = 7` cm
∴ Diameter of the toy = `2 xx r`
= `2 xx 7` cm = 14 cm
- Diameter: 14 cm
- Length (Height): 3 cm
APPEARS IN
संबंधित प्रश्न
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. What is the area of the glass?
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. How much of tape is needed for all the 12 edges?
The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at Rs. 6.60 per square metre is Rs. 5082. Find the length and breadth of the room.
Three cuboids of dimensions 5 cm × 6 cm × 7cm, 4cm × 7cm × 8 cm and 2 cm × 3 cm × 13 cm are melted and a cube is made. Find the side of cube.
A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from this block? Assume cutting causes no wastage.
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
A rectangular field is 70 m long and 60 m broad. A well of dimensions 14 m × 8 m × 6 m is dug outside the field and the earth dug-out from this well is spread evenly on the field. How much will the earth level rise?
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.
Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.
A cuboid has total surface area of 50 m2 and lateral surface area is 30 m2. Find the area of its base.
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering 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.
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
The volume of a cube whose surface area is 96 cm2, is
The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm2, find its length.
The cost of constructing a wall 8 m long, 4 m high and 10 cm thick at the rate of Rs. 25 per m3 is
10 cubic metres clay is uniformly spread on a land of area 10 ares. the rise in the level of the ground is
If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is
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.
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.
A tank 30 m long, 24 m wide, and 4.5 m deep is to be made. It is open from the top. Find the cost of iron-sheet required, at the rate of ₹ 65 per m2, to make the tank.
The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm3, find its length.
The height of a circular cylinder is 20 cm and the diameter of its base is 14 cm. Find:
(i) the volume
(ii) the total surface area.
Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm2.
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
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.
A square plate of side 'x' cm is 4 mm thick. If its volume is 1440 cm3; find the value of 'x'.
A metallic sheet is of the rectangular shape with dimensions 48cm x 36cm. From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.
The surface area of a cuboid formed by joining two cubes of side a face to face is ______.
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?
