Mensuration of Class 10
Question
An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also find the volume of water the bucket can hold. (Take π = 22/7).
An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also find the volume of water the bucket can hold. (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
