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
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?
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?
How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?
The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?
Find the surface area of a cuboid whose length = 10 cm, breadth = 12 cm, height = 14 cm.
Find the surface area of a cuboid whose length = 6 dm, breadth = 8 dm, height = 10 dm.
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 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.
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm2, find the length, the breadth and the height of the solid.
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?
Find the volume and the total surface area of a cuboid, whose :
length = 15 cm, breadth = 10 cm and height = 8 cm.
A wall 9 m long, 6 m high and 20 cm thick, is to be constructed using bricks of dimensions 30 cm, 15 cm, and 10 cm. How many bricks will be required?
A closed box is cuboid in shape with length = 40 cm, breadth = 30 cm and height = 50 cm. It is made of a thin metal sheet. Find the cost of metal sheet required to make 20 such boxes, if 1 m2 of metal sheet costs Rs. 45.
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.
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
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5: 6, find the ratio of their curved surfaces.
The diameter of a garden roller is 1.4 m and it 2 m long. Find the maximum area covered by its 50 revolutions?
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.
A square plate of side 'x' cm is 4 mm thick. If its volume is 1440 cm3; find the value of 'x'.
The dimensions of a cuboidal box are 6 m × 400 cm × 1.5 m. Find the cost of painting its entire outer surface at the rate of ₹ 22 per 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
Three identical cubes of side 4 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid
Two cuboids with equal volumes will always have equal surface areas.
A cuboidal tin box opened at the top has dimensions 20 cm × 16 cm × 14 cm. What is the total area of metal sheet required to make 10 such boxes?
