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The sum of the circumference of a circle and the perimeter of a square is equal to 272 cm. The diameter of the circle is 56 cm. What is the sum of the areas of the circle and the square?
- a)2464 sq cm
- b)2644 sq cm
- c)3040 sq cm
- d)cannot be determined
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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The sum of the circumference of a circle and the perimeter of a square...
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The sum of the circumference of a circle and the perimeter of a square...
Given information:
- The sum of the circumference of a circle and the perimeter of a square is equal to 272 cm.
- The diameter of the circle is 56 cm.
To find:
The sum of the areas of the circle and the square.
Solution:
1. Circumference of a circle:
The circumference of a circle can be calculated using the formula:
C = πd
where C is the circumference and d is the diameter.
Given that the diameter of the circle is 56 cm, we can find the circumference:
C = π * 56 = 176 cm
2. Perimeter of a square:
The perimeter of a square is given by the formula:
P = 4s
where P is the perimeter and s is the length of each side.
Let's assume that the side length of the square is 'a'.
Given that the sum of the circumference of the circle and the perimeter of the square is 272 cm, we can write the equation:
C + P = 272
Substituting the values of C and P, we have:
176 + 4a = 272
4a = 272 - 176
4a = 96
a = 24 cm
So, the side length of the square is 24 cm.
3. Area of the circle:
The area of a circle can be calculated using the formula:
A = πr²
where A is the area and r is the radius.
Given that the diameter of the circle is 56 cm, the radius is half the diameter:
r = 56/2 = 28 cm
Substituting the value of r, we have:
A = π * (28)² = 2464 cm²
4. Area of the square:
The area of a square is given by the formula:
A = s²
where A is the area and s is the length of each side.
Given that the side length of the square is 24 cm, we can calculate the area:
A = 24² = 576 cm²
5. Sum of the areas:
The sum of the areas of the circle and the square is:
2464 + 576 = 3040 cm²
Therefore, the sum of the areas of the circle and the square is 3040 cm², which corresponds to option C.
- The sum of the circumference of a circle and the perimeter of a square is equal to 272 cm.
- The diameter of the circle is 56 cm.
To find:
The sum of the areas of the circle and the square.
Solution:
1. Circumference of a circle:
The circumference of a circle can be calculated using the formula:
C = πd
where C is the circumference and d is the diameter.
Given that the diameter of the circle is 56 cm, we can find the circumference:
C = π * 56 = 176 cm
2. Perimeter of a square:
The perimeter of a square is given by the formula:
P = 4s
where P is the perimeter and s is the length of each side.
Let's assume that the side length of the square is 'a'.
Given that the sum of the circumference of the circle and the perimeter of the square is 272 cm, we can write the equation:
C + P = 272
Substituting the values of C and P, we have:
176 + 4a = 272
4a = 272 - 176
4a = 96
a = 24 cm
So, the side length of the square is 24 cm.
3. Area of the circle:
The area of a circle can be calculated using the formula:
A = πr²
where A is the area and r is the radius.
Given that the diameter of the circle is 56 cm, the radius is half the diameter:
r = 56/2 = 28 cm
Substituting the value of r, we have:
A = π * (28)² = 2464 cm²
4. Area of the square:
The area of a square is given by the formula:
A = s²
where A is the area and s is the length of each side.
Given that the side length of the square is 24 cm, we can calculate the area:
A = 24² = 576 cm²
5. Sum of the areas:
The sum of the areas of the circle and the square is:
2464 + 576 = 3040 cm²
Therefore, the sum of the areas of the circle and the square is 3040 cm², which corresponds to option C.
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The sum of the circumference of a circle and the perimeter of a square is equal to 272 cm. The diameter of the circle is 56 cm. What is the sum of the areas of the circle and the square?a)2464 sq cmb)2644 sq cmc)3040 sq cmd)cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer?
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