Advertisements
Advertisements
Question
A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?
Advertisements
Solution
Surface area of a cube = 6a2, where a is side of a cube.
... Side of cube = 5 cm
... Surface area of the cube = 6 × (5)2 = 6 × 25 = 150 cm2
Now, surface area of the cube with side 1 cm = 6 × (1)2 = 6 cm2
... Surface area of 5 cubes with side 1 cm = 5 × 6 = 30 cm2
Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes
= `30/150`
= `3/15`
= 1 : 5
APPEARS IN
RELATED QUESTIONS
Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
Find the surface area of a cube whose edge is 3 cm.
Total surface area of a cube is 864 sq.cm. Find its volume.
The edges of three cubes of metal are 3 cm, 4 cm, and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.
The internal length, breadth, and height of a box are 30 cm, 24 cm, and 15 cm. Find the largest number of cubes which can be placed inside this box if the edge of each cube is
(i) 3 cm (ii) 4 cm (iii) 5 cm
Three solid cubes of edges 6 cm, 10 cm, and x cm are melted to form a single cube of edge 12 cm, find the value of x.
The total surface area of a cube is 294cm2. Find its volume.
Three metal cubes with edges 6cm, 8cm and 10cm respectively are melted together and formed into a single cube. Find the diagonal of this cube.
A cubical container of side 6.5 m is to be painted on the entire outer surface. Find the area to be painted and the total cost of painting it at the rate of ₹ 24 per m2
The lateral surface area of a cube of side 12 cm is
