Find the sum of the radius and the perimeter of a circle with diameter of 14cm.
Find the HCF of 6p ^ 2 * q 12pq and 18p * q ^2
Which of the following numbers is divisible by 14?
1190
1530
1105
1445
3. Calculate the height of an isosceles triangle shown below.
30°
10sqrt(3) cm
1. The radius of the circle is half the diameter, so the radius is 7 cm. The perimeter of a circle is given by the formula P = 2πr, where r is the radius. So the perimeter is 2π(7) = 14π cm. The sum of the radius and the perimeter is 7 + 14π ≈ 56.57 cm.
2. To find the HCF of 6p^2*q and 12pq, we need to factorize each term. 6p^2*q = 2 * 3 * p * p * q and 12pq = 2 * 2 * 3 * p * q. The common factors are 2, 3, p, and q. So the HCF is 2 * 3 * p * q = 6pq.
3. To calculate the height of an isosceles triangle with a base angle of 30° and sides of length 10√3 cm, we can use trigonometry. The height h can be found using the sine function as sin(30°) = h / 10√3. Simplifying, we get h = 10√3 * sin(30°) = 10√3 * (1/2) = 5√3 cm. So the height of the triangle is 5√3 cm.
4. To determine which of the following numbers is divisible by 14, we need to check if each number is divisible by 2 and 7.
- 1190 is divisible by 2 (595) and 7 (170), so it is divisible by 14.
- 1530 is divisible by 2 (765) but not by 7, so it is not divisible by 14.
- 1105 is not divisible by 2 or 7, so it is not divisible by 14.
- 1445 is not divisible by 2 or 7, so it is not divisible by 14.
Therefore, the number 1190 is divisible by 14.