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Three-fourteenth (3/14)th of the radius of a circle of area 5544 sq. cm is equal to the side of a square. Area of a rectangle is equal to the area of the square. If the breadth of the rectangle is 6 cm, what is the length of the rectangle?
- a)11.5 cm
- b)9.5 cm
- c)13.5 cm
- d)Cannot be determined
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Three-fourteenth (3/14)th of the radius of a circle of area 5544 sq. ...
Π r2 = 5544 => r = 42 cm
Side of a square = (3/14) X 42 = 9 cm
Area of rectangle = area of square = 81 sq.cm
Length of the rectangle = 81/6 = 13.5 cm
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Three-fourteenth (3/14)th of the radius of a circle of area 5544 sq. ...
Given:
- Three-fourteenth (3/14)th of the radius of a circle of area 5544 sq. cm is equal to the side of a square.
- The area of a rectangle is equal to the area of the square.
- The breadth of the rectangle is 6 cm.
To find:
The length of the rectangle.
Solution:
1. Let's assume the radius of the circle is r cm.
2. The area of the circle is given as 5544 sq. cm, so we can write the equation:
πr^2 = 5544
(π is a constant, approximately equal to 22/7)
3. We need to find the side of the square, which is equal to three-fourteenth (3/14)th of the radius of the circle.
So, the side of the square = (3/14)r cm.
4. The area of the square is given by the formula: side^2
Area of the square = [(3/14)r]^2 = (9/196)r^2
5. The area of the rectangle is equal to the area of the square.
Area of the rectangle = (breadth) × (length)
6. Given that the breadth of the rectangle is 6 cm.
So, the area of the rectangle = 6 × length = 6l
7. Equating the area of the rectangle and the square:
6l = (9/196)r^2
8. Rearranging the equation, we get:
l = (9/196)r^2 ÷ 6
9. Substituting the value of r^2 from the equation of the circle:
l = (9/196)(5544/π) ÷ 6
10. Simplifying the equation:
l = (9/196)(5544/22/7) ÷ 6
l = (9/196)(252) ÷ 6
l = 9 × 3
l = 27 cm
Therefore, the length of the rectangle is 27 cm.
- Three-fourteenth (3/14)th of the radius of a circle of area 5544 sq. cm is equal to the side of a square.
- The area of a rectangle is equal to the area of the square.
- The breadth of the rectangle is 6 cm.
To find:
The length of the rectangle.
Solution:
1. Let's assume the radius of the circle is r cm.
2. The area of the circle is given as 5544 sq. cm, so we can write the equation:
πr^2 = 5544
(π is a constant, approximately equal to 22/7)
3. We need to find the side of the square, which is equal to three-fourteenth (3/14)th of the radius of the circle.
So, the side of the square = (3/14)r cm.
4. The area of the square is given by the formula: side^2
Area of the square = [(3/14)r]^2 = (9/196)r^2
5. The area of the rectangle is equal to the area of the square.
Area of the rectangle = (breadth) × (length)
6. Given that the breadth of the rectangle is 6 cm.
So, the area of the rectangle = 6 × length = 6l
7. Equating the area of the rectangle and the square:
6l = (9/196)r^2
8. Rearranging the equation, we get:
l = (9/196)r^2 ÷ 6
9. Substituting the value of r^2 from the equation of the circle:
l = (9/196)(5544/π) ÷ 6
10. Simplifying the equation:
l = (9/196)(5544/22/7) ÷ 6
l = (9/196)(252) ÷ 6
l = 9 × 3
l = 27 cm
Therefore, the length of the rectangle is 27 cm.
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Three-fourteenth (3/14)th of the radius of a circle of area 5544 sq. cm is equal to the side of a square. Area of a rectangle is equal to the area of the square. If the breadth of the rectangle is 6 cm, what is the length of the rectangle?a)11.5 cmb)9.5 cmc)13.5 cmd)Cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer?
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