If a solid metal cylinder of radius 4 cm and height 10 cm is melted to make solid balls of radius 1 mm then number of such balls produced (in lakhs) will be.
1 mm = 10^-1 cm
pi R^2 h = n (4/3)pi r^3
so
n = R^2 h / r^3 = (3/4) 4^2 * 10 / 10^-3
=12*10^4 = 120,000
I am not certain about the "lakhs" part... but
You take the total volume of the original cylinder (pi)(r^2)(h) and then divide it by the volume of each of the spheres (and make sure you have the sphere of the ball as having a radius of .1cm) so your units all match up.
Volume of sphere is (4/3)(pi)(r^3)
Your answer is very rounded....
If this is a business for money then the company would like to know exactly how many such spheres could be produced : )
Or perhaps that is the lakhs part....
Why did the solid metal cylinder go to the doctor? Because it was feeling a little "melty"!
Now, let's get down to business with a touch of humor! To find out how many solid balls with a radius of 1 mm can be produced from the metal cylinder, let's calculate the total volume of the cylinder and then divide it by the volume of one ball.
First, let's find the volume of the cylinder. The formula for the volume of a cylinder is πr^2h, where r is the radius and h is the height.
Volume of the cylinder = π × (4 cm)^2 × 10 cm
= 160π cm^3
Now, let's calculate the volume of one ball. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius.
Volume of one ball = (4/3)π × (1 mm)^3
= (4/3)π mm^3
We know that 1 cm = 10 mm, so we can convert the volume of one ball to cm^3.
Volume of one ball = (4/3)π × (1 mm)^3
= (4/3)π × (0.1 cm)^3
= (4/3)π × 0.001 cm^3
= (4/3)π × 0.001 cm^3
= (4/3) × 0.001π cm^3
Now, let's divide the volume of the cylinder by the volume of one ball to find the number of balls that can be made.
Number of balls = (Volume of cylinder) / (Volume of one ball)
= 160π cm^3 / [(4/3)π × 0.001 cm^3]
= (160 × 3) / 4 × 0.001
= 120000 / 4 × 0.001
= 30000000
So, the number of balls that can be produced is 30-million or 30 lakhs.
I hope you enjoyed this little mathematical circus act!
To find the number of balls produced, we need to calculate the total volume of the metal cylinder and then divide it by the volume of a single ball.
1. Calculate the volume of the metal cylinder:
The formula for the volume of a cylinder is V = π * r^2 * h, where r is the radius and h is the height.
Given: r = 4 cm and h = 10 cm
V = π * (4 cm)^2 * 10 cm
V = 160π cm^3
2. Convert the volume of the cylinder to liters:
1 cm^3 = 0.001 liters
Volume of the cylinder in liters = 160π cm^3 * 0.001 liters/cm^3
Volume = 0.16π liters
3. Calculate the volume of a single ball:
The formula for the volume of a sphere is V = (4/3) * π * r^3, where r is the radius.
Given: r = 1 mm = 0.1 cm
V = (4/3) * π * (0.1 cm)^3
V = (4/3) * π * 0.001 cm^3
V = 0.004π cm^3
4. Convert the volume of a single ball to liters:
Volume of a single ball in liters = 0.004π cm^3 * 0.001 liters/cm^3
Volume = 0.004π * 0.001 liters
5. Calculate the number of balls:
Number of balls = (Volume of the cylinder in liters) / (Volume of a single ball in liters)
Number of balls = (0.16π liters) / (0.004π * 0.001 liters)
Number of balls = 40,000
Since the question asks for the number of balls in lakhs, we divide the number by 100,000:
Number of balls = 40,000 / 100,000 = 0.4
Therefore, the number of balls produced will be 0.4 lakhs.
To find the number of solid balls produced from a solid metal cylinder, we need to calculate the volume of the cylinder and the volume of the individual balls.
The volume of a cylinder can be calculated using the formula: Vcylinder = πr^2h, where r is the radius and h is the height.
Given:
Radius of the cylinder: r = 4 cm
Height of the cylinder: h = 10 cm
Substituting the given values into the formula:
Vcylinder = π(4^2)(10)
= 160π cm^3
Now, let's calculate the volume of a single ball.
The volume of a sphere can be calculated using the formula: Vsphere = (4/3)πr^3, where r is the radius.
Given:
Radius of the ball: r = 1 mm = 0.1 cm (since 1 cm = 10 mm)
Substituting the given value into the formula:
Vsphere = (4/3)π(0.1^3)
= (4/3)π(0.001)
= (4/3)π(0.001) cm^3
To find the number of solid balls produced, we divide the volume of the cylinder by the volume of a single sphere and multiply it by 100,000 (to convert to lakhs):
Number of balls = (Vcylinder / Vsphere) * 100,000
= (160π / [(4/3)π(0.001)]) * 100,000
Simplifying the expression:
Number of balls = (160 * 3 * 100,000) / (4 * 0.001)
= 12,000,000 / 0.004
= 3,000,000,000
Therefore, the number of solid balls produced will be 3,000,000,000 or 300 million (in lakhs).