Question

A rectangular card-board sheet has length 32 cm and breadth 26 cm. Squares each side 3 cm are cut from the corner of the sheet and the sides are folded to make a rectangular container. Find the capacity of the container formed.
(A) 1566 cu. cm
(B) 1500 cu. cm
(C) 1530 cu. cm
(D) 1560 cu. cm

Answer 1

Hint: The length and breadth of the rectangular sheet are 32 cm and 26 cm. The squares of side 3 cm are cut from the corner of the sheet. After cutting the squares from the sheet and folding it along its sides, we get a rectangular container with the height equal to the side of the square. The length and breadth of the rectangular container is 26cm and 20 cm. Now, calculate the volume using the formula, \[\text{Volume=Length}\times \text{Breadth}\times \text{Height}\].

Complete step-by-step answer:
According to the question, it is given that a sheet is in the form of a rectangle.
The length of the rectangular sheet = 32 cm …………………………………(1)
The breadth of the rectangular sheet = 26 cm ……………………………………(2)
The squares of side 3 cm are cut from the corner of the sheet. Since a rectangle has four corners, there are four squares which are cut from the rectangular sheet.

After cutting the squares from the corners of the rectangular sheet and folding along the sides of the rectangle, we get a rectangular base with some height. In other words, we can say that we got a cuboid.
In the figure, we can see that the cuboid has FIKO as the rectangular base.
The length of the rectangular base FIKO, IK = HL- HI-KL = \[\left( 32-3-3 \right)\] cm = 26 cm ………………………………..(3)
The breadth of the rectangular base FIKO, FI = GJ – GF – IJ = \[\left( 26-3-3 \right)\] cm = 20 cm ………………………………..(4)
Since the squares of side 3 cm are cut from the corners of the sheet and the sheet is folded along the sides of the sheet. So, the height of the rectangular container is equal to the side of the square.
The height of the rectangular container = 3 cm ……………………………………….(5)
We know the formula, \[\text{Volume=Length}\times \text{Breadth}\times \text{Height}\] …………………………………(6)
Since, the rectangular container is a cuboid so, we can apply the formula of volume of a cuboid here.
From equation (3), equation (5), and equation (6), we have the length, breadth and the height of the rectangular container.
Therefore, the volume of the container = \[26cm\times 20cm\times 3cm=1560c{{m}^{3}}\] .
Hence, the correct option is (D).

Note: We can also solve this question directly.
Since, the squares of side 3 cm are being cut at the corners and folded along the side. So, the length and breadth of the rectangular container will be by two times the side of the square.
The length of the rectangular base = \[\left( 32-2\left( 3 \right) \right)\] = 32 – 6 = 26 cm.
The breadth of the rectangular base = \[\left( 26-2\left( 3 \right) \right)\] = 26 – 6 = 20 cm.
The height of the rectangular base = 3 cm.
 \[\text{Volume=Length}\times \text{Breadth}\times \text{Height}=26cm\times 20cm\times 3cm=1560c{{m}^{3}}\] .
Hence, the correct option is (D).