Ex.11.3 Q6 Mensuration Solution - NCERT Maths Class 8

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Question

Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?

 Video Solution
Mensuration
Ex 11.3 | Question 6

Text Solution

What is Known?

Shape and their respective dimension.

What is unknown?

Lateral surface area.

Reasoning:

Length of rectangular strip will be equal to the circumference of the circle. Visually, all the faces of a cube and square are equal in shape. This makes length, height and width of a cube equal, so area of each of the face will be equal.

Steps:

Similarly, both the figures are alike in respect of their same height.

The difference between the two figures is that one is cylinder and other is a cube. 

Length of one side of cube \(\,(l) = 7\, \rm{cm}\)

Height of one side of cube \(\,(h) = 7\, \rm{cm}\)

Width of one side of cube \(\,(b) = 7\, \rm{cm}\)

Lateral surface area of the cube

\[\begin{align}&= (h\! \times\! l \!+\! h\! \times\! b\!+\! h\! \times \!l \!+\! h\! \times\! b)\\ &= (l\! \times\! l \!+\! l \!\times\! l\! +\! l \times l \!+ \! l \times l)\\&\qquad \because \{ l \!= \!h \!=\! b\} \\&= 4{l^2}\\ &= 4 \times {(7)^2}\\&= 196\,{{\rm{m}}^2} \end{align}\]

Height of the cylinder \(h = 7\,\rm{cm}\)

Radius of the cylinder

\[\begin{align}r = \frac{7}{2}\,\rm{cm} = 3.5\,\rm{cm} \end{align}\]

Lateral surface area of the cylinder 

\[\begin{align}&= 2\pi rh\\&= 2 \times \frac{{22}}{7} \times 3.5 \times 7\\&=154\, \rm{m^2} \end{align}\]

Hence, the cube has larger lateral surface area.

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