Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given that:
Diagonal of cuboid = `3sqrt(29)"cm"`...............................(1)
Ratio of Length, breadth & height = 2 : 3 : 4
∴ Length (l) = 2x
Breadth (b) = 3x &
Height (h) = 4x
We know that:
Diagonal of cuboid
= `sqrt("l"^2 + "b"^2 + "h"^2)`
= `sqrt((2x)^2 + (3x)^2 + (4x)^2)`
= `sqrt(4x^2 + 9x^2 + 16x^2)`
= `sqrt(29x^2)`
= `xsqrt(29)`
Also,
`xsqrt(29) = 3sqrt(29)` ...[From (1)]
i.e., x = `(3sqrt(29))/sqrt(29)`
∴ x = 3cm
Thus,
Length = 2 x 3 = 6cm
Breadth = 3 x 3 = 9cm
Height = 4 x 3 = 12cm
∴ Volume of cuboid
= l x b x h
= 6 x 9 x 12
= 54 x 12
= 648cm3.
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.
An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 m. Find the cost of painting the inner surface of Rs 50 per sq. metre.
Find the weight of solid rectangular iron piece of size 50 cm × 40 cm × 10cm, if 1 cm3 of iron weighs 8 gm.
The volume of a cuboidal box is 48 cm3. If its height and length are 3 cm and 4 cm respectively, find its breadth.
How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
A swimming pool is 250 m long and 130 m wide. 3250 cubic metres of water is pumped into it. Find the rise in the level of water.
The central hall of a school is 80 m long and 8 m high. It has 10 doors each of size 3 m × 1.5 m and 10 windows each of size 1.5 m × 1 m. If the cost of white-washing the walls of the hall at the rate of Rs 1.20 per m2 is Rs 2385.60, fidn the breadth of the hall.
The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm. The box is made of 1.5 cm thick wood. How many bricks of size 6 cm × 3 cm × 0.75 cm can be put in this box?
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
