Advertisements
Advertisements
Question
Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is ______.
Options
1 : 4
1 : 8
1 : 16
1 : 32
Advertisements
Solution
Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is 1 : 16.
Explanation:
Let a and b be the edges of the two cubes, respectively.
Then, according to the question,
a3 : b3 = 1 : 64 ...[∵ Volume of cube = (Edge)3]
⇒ `a^3/b^3 = 1/64`
⇒ `(a/b)^3 = (1/4)^3`
⇒ `a/b = 1/4` ...[Taking cube roots on both sides]
Now, ratio of areas, `(a/b)^2 = (1/4)^2` ...[∵ Surface area of cube = 6 × (Edge)2]
⇒ `a^2/b^2 = 1/16`
∴ a2 : b2 = 1 : 16
APPEARS IN
RELATED QUESTIONS
What will be the volume of a cube having length of edge 7.5 cm?
Find the volume of a cube whose side is 3.5 m
A cubical milk tank can hold 125000 litres of milk. Find the length of its side in metres
Find the number of bricks of dimension 20 cm × 5 cm × 10 cm required to construct a wall of dimension 300 cm × 200 cm × 20 cm
How long is the side of your cube? ______
Anan made a big cube having double the side of your paper cube. How many of your paper cubes will fit in it? Try doing it by collecting all the cubes made in your class.
Ganesh and Dinga want to pack 4000-centimeter cubes inboxes. These are to be sent to a school. There are three different boxes available for packing.
Use Ganesh's method and write:
- _____ centimeter cubes can be arranged in box B.
- _____ centimeter cubes can be arranged in box C.
- So _____ centimeter cubes in all can be packed in the three boxes.
The volume of a cube whose edge is 3x is ______.
What will happen to the volume of the cube, if its edge is tripled?
What will happen to the volume of the cube, if its edge is reduced to one-fourth?
