Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
Solution:
Let's look into the open structure of the given cube and cylinder as shown below.
The length of the rectangular strip will be equal to the circumference of the circle. Visually, all the faces of a cube are square in shape. This makes the length, height, and width of a cube equal, so the area of each of the faces will be equal.
Similarly, both the figures are alike with respect to their same height that is 7cm.
The difference between the two figures is that one is a cylinder and the other is a cube.
Length of one side of cube l = 7 cm
Height of one side of cube h = 7 cm
Width of one side of cube b = 7 cm
Lateral surface area of the cube = (h × l + h × b + h × l + h × b)
= (l × l + l × l + l × l + l × l) [∵ l = h = b]
= 4 l² = 4 × (7)² = 196 cm²
Height of the cylinder h = 7 cm
Radius of the cylinder r = 7/2 cm = 3.5 cm
The lateral surface area of the cylinder = 2πrh
= 2 × 22 / 7 × 3.5 × 7 = 154 cm²
The cube with side 7cm has a greater lateral surface area.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 11
Video Solution:
Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
Maths NCERT Solutions Class 8 Chapter 11 Exercise 11.3 Question 6
Summary:
Both the figures are alike with respect to their same height that is 7cm. The difference between the two figures is that one is a cylinder and the other is a cube. The cube with side 7cm has a larger lateral surface area.
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