A closed cylindrical tank of radius 3.5 m and height 2m is made from
a sheet of metal. How much sheet of metal is required ?
Answers
Given :
Cylindrical tank
- Radius = 3.5 m
- Height = 2m
To Find :
Amount of metal sheet required to make it
Formula :
Total surface area of a cylinder is 2πr(r+h)
Solution :
Putting up the values at correct places :
➸ 2 x 22/7 x 3.5( 2 + 3.5)
➸ 2 x 22 x 0.5(2+3.5) { 3.5/7 = 0.5}
➸ 44 x 0.5 x 5.5
➸ 121 sq.m
How did we derive the formula ?
We know that a cylinder is made up of 2 circles and 1 rectangle which is curved up .
➸ We have learnt that the area of 1 circle is :
πr²
2 circles make :
πr² + πr²
➸ We have also learnt that the area of a rectangle is (l x b) . Here another logic to be applied is that the length of the rectangle is the circumference of the cylinder being constructed .
So instead of repeating length we can consider the formula of circumference as
2πr
Now when we are aware that the breadth of the rectangle is the height of cylinder formed ; we conclude the area of the rectangle in the cylinder as :
2πr × h
➸ Adding up both the formulas we get :
2πr² + 2πrh
➸ It can be modified by taking the common term as :
2πr(r+h)
Answer:
Two numbers are:
Smaller number = ± 4
Larger number = 8
Step-by-step explanation:
Given that:
The sum of squares of two numbers is 80.
The square of the smaller number is 2 times the larger number.
To Find:
The two numbers.
Let us assume:
Smaller number be x.
Larger number be y.
According to the question.
Square of the smaller number = 2 times the larger number
⟶ x² = 2y
⟶ y = x²/2 _____(i)
Sum of squares of two numbers = 80
⟶ x² + y² = 80
Substituting the value of y.
⟶ x² + (x²/2)² = 80
⟶ x² + x⁴/4 = 80
Taking 4 common in LHS.
⟶ (4x² + x⁴)/4 = 80
Cross multiplication.
⟶ 4x² + x⁴ = 80 × 4
⟶ 4x² + x⁴ = 320
⟶ x⁴ + 4x² - 320 = 0
⟶ (x²)² + 4x² - 320 = 0
⟶ (x²)² + 20x² - 16x² - 320 = 0
⟶ x²(x² + 20) - 16(x² + 20) = 0
⟶ (x² - 16) (x² + 20) = 0
⟶ x² = 16 or x² = - 20 (complex number)
⟶ x = √16
⟶ x = ± 4
In equation (i).
When x = 4
⟶ y = x²/2
⟶ y = (4)²/2
⟶ y = 16/2
⟶ y = 8
When x = - 4
⟶ y = x²/2
⟶ y = (- 4)²/2
⟶ y = 16/2
⟶ y = 8
We get that:
Smaller number = ± 4
Larger number = 8