Area Related To Circles of Class 10
Question
A horse is tied to a pole M at middle of the side AB of a square shaped grass field of side 50 m by means of a 7 m long rope (figure). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10.5 m long instead of 7 m.
(iii) the grazing area if the rope is 10.5 long and the horse is tied to a pole at the corner A instead of M. (Take π = 22/7)
A horse is tied to a pole M at middle of the side AB of a square shaped grass field of side 50 m by means of a 7 m long rope (figure). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10.5 m long instead of 7 m.
(iii) the grazing area if the rope is 10.5 long and the horse is tied to a pole at the corner A instead of M. (Take π = 22/7)
Frequently Asked Questions
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A two digit number is 4 times the sum of its digits and twice
the product of its digits.The number is - - - - - -
Solution:
Explanation:
Let x be the digit in the ones place and y be the digit in the tens place, resulting in the two-digit number = 10 y + x..
Given that the sum of the digits of a two-digit integer equals four,
According to the question
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Final Answer:
The number is 36.
The angle of elevation of the top of a tower from a point on the ground
which is 30m away from the foot of the tower, is 30∘. Find the height of the tower.
Solution:
Explanation:
Let us take the height of the tower to be AB
Let C be the point elevation which is 30m away from the foot of the tower
We know that for a given right angled triangle,
Final Answer:
The height of the tower : 10 Root 3m
Prove that the product of three consecutive positive integers is divisible by 6
Solution:
Explanation:
Let us take the three consecutive positive integers as : a,a + 1,a + 2
A number when divided by 3, will have a remainder = 0 or 1 or 2
We can clearly see the numbers a,a + 1,a + 2 are always divisible by 3.
Similarly, we can show that when a number is divisible by 2, we get the remainder as 0 or 1
Clearly, 2m and 2(m+1) both are divisible by 2.
We can clearly see the numbers a,a + 1,a + 2 are always divisible by 2.
We can say that a,a + 1,a + 2 is always divisible by 2 ,3 ,6
Example:
Let us take: 3,4,5
3 x 4 x 5 = 60
We can see that 60 is divisible by 6
