Question

Q.8 A teacher wants to measure the
density of a wooden cylinder. She
measures the radius, height and mass
of the cylinder. Which of the
measurements that she has taken are
required to calculate the density of
the cylinder? *​

Answer 1

Answer:

Required Answer :-

Yes, she should take measurement

$\tiny \checkmark$

Reason :-

According to the formula

P = M/V

P is the Density

M is the Mass

V is the Volume

Now,

When she will find measurements of Radius, height then she will find volume and after she will divide the Mass by Volume.

The formula for finding volume will be

Volume = πr²h

π = 22/7

r = Radius

H = Height

Answer 2

All the measurements are indispensable, i.e., all are required.

We know,

$\boxed{\rho = \dfrac{M}{V}}$

Clearly, mass is very important for the calculation. But, question arises that why did the teacher took the measurement of radius and height.

Since the object was of cylindrical shape, and we know,

$V = \pi r^2 h$ (right circular cylinder)

∴ $\rho = \dfrac{M}{(\pi r^2 h)}$.

N.B.:-

Terms used in formulae are usual terms.

More:-

Formula of hollow,

• Cylinder = $\pi h (R^2 - r^2) = \pi h (R + r)(R - r)$.
• Sphere = $\dfrac{4}{3} \pi (R^3 - r^3)$.
• Cube = $A^3 - a^3$.
• Cuboid = $LBH - lbh$.

Basic thing: Even if you do not know the formulae, you can think that to subtract the smaller object from the bigger one.