A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in Fig. 9.52: Does the perimeter change? If it does change, by how much does it increase or decrease?
Solution:
We know that
Curved part of the new shape is 1/4th the perimeter of the circle and the radius is the straight line
It is given that
Radius of the original circle = 16 cm
Perimeter = 2πr
Substituting the values
= 2π × 16
= 32π
Perimeter of curved part of new shape = 1/4 × 32π = 8π
Here
Perimeter of new shape = (4 × Perimeter of curved part) + (2 × radius)
Substituting the values
= (4 × 8π) + (2 × 16)
= 32π + 32
Perimeter is increased by 32 cm.
Therefore, the perimeter of the circle increases by 32 cm.
✦ Try This: The perimeter of a rhombus is 80 cm and one diagonal is 8 cm long then the length of the other diagonal is
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 100
A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in Fig. 9.52: Does the perimeter change? If it does change, by how much does it increase or decrease?
Summary:
A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in Fig. 9.52. Yes, the perimeter changes. The perimeter is increased by 32 cm.
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