Advertisements
Advertisements
प्रश्न
The length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
Advertisements
उत्तर
Surface area of cuboid = 2548 cm2
Ratio in length, breadth and height of a cuboid = 4 : 3 : 2
Let length = 4x, Breadth = 3x and height = 2x
`therefore "Surface area" = 2(4x xx 3x + 3x xx 2x + 2x xx 4x)`
= `2(12x^2 + 6x^2 + 8x^2)`
= `2 xx 26x^2 = 52x^2`
`therefore 52x^2 = 2548`
`x^2 = 2548/52 = 49 = (7)^2`
`therefore x = 7`
`therefore "Length" = 4x = 4 xx 7 = 28` cm
`therefore "Breadth" = 3x = 3 xx 7 = 21` cm
`"and height" = 2x = 2 xx 7 = 14`cm
`therefore "Volume" = lbh`
`= 28 xx 21 xx 14` cm3 = 8232 cm2
(ii) If volume = 3000 m3
⇒ `4x xx 3x xx 2x = 3000`
⇒ `24x^3 = 3000`
⇒ `x^3 = 3000/24 = 125 = (5)^3`
`therefore x = 5`m
`"Length" = 5 xx 4 = 20, "breadth" = 5 xx 3 = 15`m
and height = `5 xx 2 = 10`m
`therefore "Surface area" = 2[lb + bh + hl]`
= `2[20 xx 15 + 15 xx 10 + 10 xx 20]`m2
= `2[300 + 150 + 200]`m2
= `2 xx 650 = 1300`m2
APPEARS IN
संबंधित प्रश्न
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 per m2.
The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
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?
Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of the reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?
A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 litres of milk?
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.
The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.
A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?
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.
A cuboid has total surface area of 50 m2 and lateral surface area is 30 m2. Find the area of its base.
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.
Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is
The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is ` 5 sqrt(5)` cm. Its surface area is
If l is the length of a diagonal of a cube of volume V, then
Find the volume and the total surface area of a cuboid, whose :
l = 3.5 m, b = 2.6 m and h = 90 cm
The volume of a cuboid is 3456 cm3. If its length = 24 cm and breadth = 18 cm ; find its height.
The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If the volume of the cuboid is 1.92 m3; find its length.
Find the volume and total surface area of a cube whose each edge is:
(i) 8 cm
(ii) 2 m 40 cm.
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 external dimensions of an open wooden box are 65 cm, 34 cm, and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.
The diameter of a garden roller is 1.4 m and it 2 m long. Find the maximum area covered by its 50 revolutions?
An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust-proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?
How much sheet metal is required to make a closed rectangular box of length 1.5 m, breadth 1.2 m, and height 1.3 m?
Find the Total Surface Area and the Lateral Surface Area of a cuboid whose dimensions are: length = 20 cm, breadth = 15 cm, height = 8 cm
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?
Three cubes each of side 10 cm are joined end to end. Find the surface area of the resultant figure.
