Advertisements
Advertisements
Question
A 4 cm edge cube is cut into 1 cm edge cubes. Calculate the total surface area of all the small cubes.
Advertisements
Solution
Edge of cube = 4 cm
Volume of 4 cm cube = (4 cm)3 = 64 cm3
Edge of cube = 1 cm
Volume of 1 cm cube = (1 cm)3
∴ Total number of small cubes = `(64 cm^3)/(1 cm^3) = 64`
∴ Total surface area of 64 cm all cubes
= 64 × 6 × (1 cm)2
= 384 cm2
The total surface area of all the small cubes formed by cutting the 4 cm cube into 1 cm edge cubes is 384 cm2.
RELATED QUESTIONS
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
 |
 |
| (a) | (b) |
Ravish wanted to make a temporary shelter for his 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 × 3m?
The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.
Find the volume in cubic metre (cu. m) of the cuboid whose dimensions is length = 10 m, breadth = 25 dm, height = 50 cm.
How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
Find the surface area of a cuboid whose length = 6 dm, breadth = 8 dm, height = 10 dm.
A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
The dimensions of an oil tin are 26 cm × 26 cm × 45 cm. Find the area of the tin sheet required for making 20 such tins. If 1 square metre of the tin sheet costs Rs 10, find the cost of tin sheet used for these 20 tins.
The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm, respectively. Find the cost of plastering at the rate of Rs 8 per square metre.
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 breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its dimensions.
The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 m3 of air?
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is
The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is ` 5 sqrt(5)` cm. Its surface area is
The volume of a cuboid is 7.68 m3. If its length = 3.2 m and height = 1.0 m; find its breadth.
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5: 6, find the ratio of their curved surfaces.
An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust-proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?
A room is 22m long, 15m broad and 6m high. Find the area of its four walls and the cost of painting including doors and windows at the rate of Rs.12per m2.
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?
