A cube of side 6 cm is painted on all its faces and then cut into smaller cubes each of side 2 cm. Find the number of cubes which have exactly two faces painted.
12
Cutting a 6 cm cube into 2 cm cubes gives \(\frac{6}{2} = 3\) divisions per edge, so a total of \(3\times3\times3 = 27\) small cubes.
Small cubes with exactly two painted faces lie along the edges of the big cube, excluding the corner cubes. Each edge of the big cube has \((3-2) = 1\) such cube.
A cube has 12 edges, so the number of small cubes with exactly two faces painted is \(12\times1 = 12\).
There are 12 such small cubes.
Similar Questions
A cubical tank of side 10 m is open at the top. The inner surfaces of the tank including its base are to be painted at the rate of ₹5 per square metre. Find the total cost of painting.
A solid cylinder has a radius of 7 cm and height of 10 cm. Find its total surface area. (Use \(\pi = \dfrac{22}{7}\))
Important Questions from Mensuration (Teaching)
- The base diameter of a cylinder is 21 cm and the height is 28 cm, then:
(A) Radius of cylinder = 10.5 cm
(B) Volume = 12936 cm³
(C) Curved Surface Area = 1848 cm²
(D) Total surface area = 2541 cm²
Which of the following is/ are correct?
Choose the correct answer from the options given below: - On the basis of the information given in the statement, which of the suggested course of action logically follows ?
Statement : Anamika does conceptual error while solving problems on mensuration.
Course of Action :
(I) Teacher gives a lot of hands-on and visual practice to Anamika.
(II) Teacher provides the scope of discussion while giving open-ended questions.
Choose the correct option. - A teacher asked the children to cut out six squares of 'one' unit each and then asked, "How many different shapes can you make using these squares? Which shape formed would have the maximum perimeter?" The least appropriate objective of this activity is
- The numerical values of perimeter and area of a square are equal. The length of the side of the square is :
A cubical tank of side 10 m is open at the top. The inner surfaces of the tank including its base are to be painted at the rate of ₹5 per square metre. Find the total cost of painting.
