Advertisements
Advertisements
प्रश्न
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
पर्याय
7 : 9
49 : 81
9 : 7
27 : 23
Advertisements
उत्तर
Let, a → Side of each cube
So, the dimensions of the resulting cuboid are,
Length(l) = 3a
Breadth (b) = a
Height (h) = a
Total surface area of the cuboid,
=2(lb + bh + hl)
=2[(3a) a + a × a + a (3a)]
= 14 a2
Sum of the surface areas of the three cubes,
= 3 (6a2)
= 18 a2 Required ratio,
=`(14a^2)/(18a^2)`
=7:9
Thus, the required ratio is 7: 9 .
APPEARS IN
संबंधित प्रश्न
Find the volume of a cuboid whose length = 15 cm, breadth = 2.5 dm, height = 8 cm.
The volume of a cuboidal box is 48 cm3. If its height and length are 3 cm and 4 cm respectively, find its breadth.
A rectangular water reservoir contains 105 m3 of water. Find the depth of the water in the reservoir if its base measures 12 m by 3.5 m.
The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square metre is Rs 340.20 and the cost of matting the floor at 85 paise per square metre is Rs 91.80. Find the height of the room.
If l is the length of a diagonal of a cube of volume V, then
A solid cube of edge 14 cm is melted down and recast into smaller and equal cubes each of the edge 2 cm; find the number of smaller cubes obtained.
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 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?
In a building, there are 24 cylindrical pillars. For each pillar, the radius is 28 m, and the height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.
