Mathematics
Consider the following two statements:
Statement 1: If the circumference of a circle is 10π cm, then its area is 25π cm2.
Statement 2: The area of a circle is π times its circumference.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Mensuration
1 Like
Answer
Given that the circumference is 10π cm.
⇒ 2πr = 10π
⇒ r =
⇒ r = 5 cm
Now, calculate the area using this radius,
⇒ A = πr2
= π.52
= 25π cm2.
∴ Statement 1 is true.
We know that,
Circumference of the circle = 2πr
2πr × π = 2π2r ≠ πr2.
∴ Statement 2 is false.
∴ Statement 1 is true, and Statement 2 is false.
Hence, option 3 is the correct option.
Answered By
3 Likes
Related Questions
A cuboid container has the capacity to hold 50 small boxes. If all the dimensions of the container are doubled, then it can hold (small boxes of same size)
100 boxes
200 boxes
400 boxes
800 boxes
The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit which is 16 m long, 12 m wide and 4 m deep is
1900
1920
1800
1840
Assertion (A): Sides of a triangle are 9 cm, 12 cm and 15 cm. This triangle is both scalene triangle and right angle triangle.
Reason (R): Area of a right triangle = x base x height.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Assertion (A): Heron's formula can be used to find the area of a scalene triangle only.
Reason (R): If ABC is a triangle with side a, b and c respectively, then its area = , where s = .
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).