Ex.11.3 Q6 Mensuration Solution - NCERT Maths Class 8

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

 Video Solution
Ex 11.3 | Question 6

Text Solution

What is Known?

Shape and their respective dimension.

What is unknown?

Lateral surface area.


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.


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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