Advertisements
Advertisements
Question
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
Options
7 : 9
49 : 81
9 : 7
27 : 23
Advertisements
Solution
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
RELATED QUESTIONS
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?
Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth, and height of 15 m, 10 m, and 7 m, respectively. From each can of paint, 100 m2 of area is painted. How many cans of paint will she need to paint the room?
The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at Rs. 6.60 per square metre is Rs. 5082. Find the length and breadth of the room.
How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage?
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
The total surface area of a cube is 216 cm2. Find its volume.
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
Below are the drawings of cross sections of two different pipes used to fill swimming pools. Figure A is a combination of 2 pipes each having a radius of 8 cm. Figure B is a pipe having a radius of 15 cm. If the force of the flow of water coming out of the pipes is the same in both the cases, which will fill the swimming pool faster?
