Calculate the area and perimeter of the following rings where a = 7cm, b = 14cm Area of both Rings: Perimeter of Rings: iii. Area of shaded part of both rings
Answers
Answer:
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Step-by-step explanation:
Area of both Rings:
• Area of circle = πr²
Area of ring = πr² = 22/7 × 7 × 7 cm²
Area of ring = πr² = 22/7 × 7 × 7 cm² = 154 cm²
• Area of circle = πr²
Area of ring = πr² = 22/7 × 14 × 14 cm²
Area of ring = πr² = 22/7 × 14× 14 cm² = 616 cm²
Perimeter of Rings:
• Circumference of circle = 2πr
Perimeter of ring = 2πr = 2 × 22/7 × 7
Perimeter of ring = 2πr = 2 × 22/7 × 7 = 44 cm
• Circumference of circle = 2πr
Perimeter of ring = 2πr = 2 × 22/7 × 14
Perimeter of ring = 2πr = 2 × 22/7 × 14 = 88 cm
iii. Area of shaded part of both rings:
As you know they are concentric circles
AREA OF CIRCLE= pi×r²
PERIMETER OF A CIRCLE= 2×pi×r
so we will solve the circle which is closer to the centre(a=7)
Area- pi×r²
=22/7×7²
=22/7×7×7
=22×7(because the 7 cuts the 7)
=154cm²
PERIMETRE- 2× pi× r
=2×22/7× 7
=2×22(because the 7 cuts the 7)
=44cm
now we will solve the second circle with radii 14cm
Area= pi× r²
= 22/7× 14×14
=22×2×14(because 7 cuts 14 into 2(14/7=2))
=616cm²
Perimetre=2×pi×r
=2×22/7×14
=2×22×2(14/7=2)
=88cm
Now we have to find the area of the shaded ring so its so easy now just subtract both circles area
=616-154=462
so this means that the shaded ring's area is 462cm².......
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Given : a ring inner radius = 7 cm & outer radius = 14 cm
To find : Area of Ring and Perimeter of Ring: 132 cm
Solution:
Area of circle = π Radius²
Perimeter of circle = 2π Radius
Area of ring
= Area of bigger circle - area of smaller circle
= π (14)² - π (7)²
= π(14 + 7)(14 - 7)
= π(21)(7)
use π = 22/7
= (22/7)(21)(7)
= 462 cm²
Perimeter of ring
Area of bigger circle + area of smaller circle
= 2π(14) + 2π(7)
= 2π(21)
= 2(22/7)(21)
= 132 cm
Area of Ring: 462 cm²
Perimeter of Ring: 132 cm
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