Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
1 : 4
1 : 8
1 : 16
1 : 32
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the volume of a cube whose side is 3.5 m
How many sack of dimension 15 cm × 45 cm × 90 cm filled with rice can be kept in a room of dimension 3 m × 18 m × 9 m
Answer Thimpu's questions:
- To make the first layer on the table how many cm cubes will I use? ______
- How many such layers will I need to make a 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.
- What is your guess? Who is right?
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 ______.
Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is ______.
A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ______.
What will happen to the volume of the cube, if its edge is tripled?
