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Diameter of two circular plates are respectively 18cm and 80 cm. The diameter of the plate which has an area equal to the combined area of two given plates is
- a)98 cm
- b)40 cm
- c)41 cm
- d)82 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Diameter of two circular plates are respectively 18cm and 80 cm. The d...
Combined area of two plates = π (9)2 + π (40)2
= π (81 + 1600)
= 1681 π cm2.
Let R be the Radius of plate, whose area is combined area of two plates.
Area of plate = πR2 = 1681 π
⇒ R2 = 1681
⇒ R = 41 cm.
Diameter = 2 x 41 = 82 cm
= π (81 + 1600)
= 1681 π cm2.
Let R be the Radius of plate, whose area is combined area of two plates.
Area of plate = πR2 = 1681 π
⇒ R2 = 1681
⇒ R = 41 cm.
Diameter = 2 x 41 = 82 cm
Most Upvoted Answer
Diameter of two circular plates are respectively 18cm and 80 cm. The d...
Given Data:
- Diameter of first circular plate = 18 cm
- Diameter of second circular plate = 80 cm
Formula:
- Area of a circle = πr²
- Diameter of a circle = 2r
Calculation:
1. Area of the first circular plate:
- Radius of the first plate (r1) = Diameter / 2 = 18 / 2 = 9 cm
- Area of the first plate = π(9)² = 81π cm²
2. Area of the second circular plate:
- Radius of the second plate (r2) = Diameter / 2 = 80 / 2 = 40 cm
- Area of the second plate = π(40)² = 1600π cm²
3. Combined area of two plates:
- Combined area = 81π + 1600π = 1681π cm²
4. Diameter of the plate with the same area:
- Let the radius of the required plate be r
- Area of the required plate = πr²
5. Equating the areas:
- πr² = 1681π
- r² = 1681
- r = √1681 = 41 cm
Therefore, the diameter of the plate which has an area equal to the combined area of the two given plates is 2 * 41 = 82 cm.
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Diameter of two circular plates are respectively 18cm and 80 cm. The diameter of the plate which has an area equal to the combined area of two given plates isa)98 cmb)40 cmc)41 cmd)82 cmCorrect answer is option 'D'. Can you explain this answer?
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