Advertisements
Advertisements
प्रश्न
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is 12 `sqrt(3)` cm. Find the edges of three cubes.
Advertisements
उत्तर
The edges of the three cubes are in the ratio 3 : 4 : 5.
So, let the edges be 3x cm, 4x cm, 5x cm.
The diagonal of new cube is `12sqrt(3) `cm
We need to find the edges of three cubes
Here, volume of the resulting cube,
`V = (3x)^3 + (4x)^3 + (5x)^3`
`=27x^3 + 64x^3 + 125x^3`
`= 216x^3`
Let,
l → Edge of the resulting cube
So, diagonal of the cube`= sqrt(3l)`, so
`12sqrt(3) = sqrt(3l)`
Hence,
l = 12 cm
Now;
`V=1^3`
`216x^3 = 12^3`
`(6x)^3 = 12^3`
x = 2
The edges of the three cubes are,
3x = 3× 2
= 6cm
4x = 4× 2
= 8 cm
5x = 5 × 2
= 10 cm
The edges of the three cubes are 6 cm , 8 cm and 10 cm .
APPEARS IN
संबंधित प्रश्न
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.
The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the
flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.
Find the surface area of a cuboid whose length = 10 cm, breadth = 12 cm, height = 14 cm.
A field is 150 m long and 100 m wide. A plot (outside the field) 50 m long and 30 m wide is dug to a depth of 8 m and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?
If l is the length of a diagonal of a cube of volume V, then
A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) the total surface area of the cuboid.
(iii) the total surface area of the cube.
(iv) which of these two has a greater surface and by how much?
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.
A closed box is made of wood 5 mm thick. The external length, breadth and height of the box are 21 cm, 13 cm and 11 cm respectively. Find the volume of the wood used in making the box.
