Advertisements
Advertisements
प्रश्न
The length breadth and height of a cuboid are in the ratio of 3 : 3 : 4. Find its volume in m3 if its diagonal is `5sqrt(34)"cm"`.
उत्तर
Given that:
Diagonal of cuboid = `5sqrt(34)"cm"` ..................................(1)
Ratio of Length, breadth & height = 3 : 3 : 4
∴ Length (l) = 3x
Breadth (b) = 3x &
Height (h) = 4x
We know that:-
Diagonal of cuboid
= `sqrt("l"^2 + "b"^2 + "h"^2`
= `sqrt((3x)^2 + (3x)^2 + (4x)^2)`
= `sqrt(9x^2 + 9x^2 + 16x^2)`
= `sqrt(34x^2)`
= `xsqrt(34)`
Also,
`xsqrt(34) = 5sqrt(34)` ...[From (1)]
i.e., x = `5sqrt(34)/(sqrt(34)`
∴ x = 5cm
Thus,
Length = 3 x 5 = 15cm
Breadth = 3 x 5 = 15cm
Height = 4 x 5 = 20cm
∴ Volume of cuboid
= l x b x h
= 15 x 15 x 20
= 225 x 20
= 4500cm3
= 0.0045m3 . ...[∵ 1m3 = 106cm3]
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?
An ice-cream brick measures 20 cm by 10 cm by 7 cm. How many such bricks can be stored in deep fridge whose inner dimensions are 100 cm by 50 cm by 42 cm?
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
Find the area of the cardboard required to make a closed box of length 25 cm, 0.5 m and height 15 cm.
If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is
The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is ______.
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then `A/V`
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
A closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick; find :
(i) the capacity of the box ;
(ii) the volume of metal-sheet and
(iii) weight of the box, if 1 cm3 of metal weighs 3.6 gm.
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.
