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
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?
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.
Ravish wanted to make a temporary shelter for his 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 × 3m?
A cuboidal block of silver is 9 cm long, 4 cm broad and 3.5 cm in height. From it, beads of volume 1.5 cm3 each are to be made. Find the number of beads that can be made from the block.
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is
Total surface area of a box of cuboid shape is 500 sq. unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box ?
The volume of a cuboid is 3456 cm3. If its length = 24 cm and breadth = 18 cm ; find its height.
