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 plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m2 costs Rs 20.
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?
Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block
covered with coloured paper with picture of Santa Claus on it. She must know the exact
quantity of paper to buy for this purpose. If the box has length, breadth and height as 80
cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would
she require?
Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.
A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs. 5 per metre sheet, sheet being 2 m wide.
Find the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm.
Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively.
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 tea-packet measures 10 cm × 6 cm × 4 cm. How many such tea-packets can be placed in a cardboard box of dimensions 50 cm × 30 cm × 0.2 m?
A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there is no wastage of wood in this process. If one edge of the beam is 0.5 m, find the third edge.
The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m2. Find the dimensions.
The dimensions of an oil tin are 26 cm × 26 cm × 45 cm. Find the area of the tin sheet required for making 20 such tins. If 1 square metre of the tin sheet costs Rs 10, find the cost of tin sheet used for these 20 tins.
The perimeter of a floor of a room is 30 m and its height is 3 m. Find the area of four walls of the room.
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that \[\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)\]
A tank open at the top is made of iron sheet 4 m wide. If the dimensions of the tank are 12 m × 8 m × 6 m, find the cost of iron sheet at Rs 17.50 per metre.
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 each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
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
75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m3 of the air; find the height of the room.
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 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 total surface area of a cylinder is 6512 cm2 and the circumference of its bases is 88 cm. Find:
(i) its radius
(ii) its volume
The length, breadth, and height of a rectangular solid are in the ratio 6 : 4 :3. If the total surface area is 1728 cm2. Find its dimensions.
A room is 22m long, 15m broad and 6m high. Find the area of its four walls and the cost of painting including doors and windows at the rate of Rs.12per m2.
The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of white washing the walls and ceiling at the rate of ₹ 8.50 per m2
