Question

A cylindrical hole of diameter $ 30\;cm $ is bored through a cubical wooden block with side $ 1 $ metre as shown in the figure. Find the volume of the object so formed. $ (\pi = 3.14) $

Answer 1

Hint: Here, we will use the formulas to find the volume of the cube and cylinder. Find the difference of both the volumes to get the volume of the formed object. Convert units of the terms where applicable.

Complete step-by-step answer:

Given that the diameter of the cylinder is $ d = 30\;cm $
Radius of the cylinder is $ r = \dfrac{d}{2} $
Place the values –
 $ \Rightarrow r = \dfrac{{30}}{2} = 15\;cm $
Convert all the given units in the same system of units.
Therefore convert centimetres into metres.
 $ \Rightarrow r = 15\;cm = 0.15\;m $
Now, the height of the cylinder is equal to the side of the cube.
Height, $ h = 1m $
Side of cube, $ l = 1\;m $
Volume of the cube is equal to the cube of its sides.
 $ V = {l^3} $
Place values in the above equation –
 $
  V = {(1)^3} \\
   \Rightarrow V = 1\;{m^3}\;{\text{ }}.....{\text{ (A)}} \;
  $
Similarly find the volume for the cylinder -
 Volume of the cylinder $ = \pi {r^2}h $
Place values of the radius and the height in the above equation.
 $ V = (3.14) \times {(0.15)^2} \times 1m $
Simplify the above equation-
 $ V = 3.14 \times 0.0225 \times 1 $
Simplification –
 $ V = 0.07065\;{m^3} $ ..... (B)
Now, the volume of an object is the difference of the volume of the cube and the cylinder.
Volume of an object $ = $ Volume of the cube – volume of the cylinder
Place values by using the equations (A) and (B)
Volume of an object $ = 1 - 0.07065 $
Volume of an object $ = 0.92935\;{m^3} $
The required answer – the volume of an object is $ 0.92935\;{m^3} $
So, the correct answer is “ $ 0.92935\;{m^3} $ ”.

Note: Always check the units of all the given terms. All the terms should be in the same system of units. Remember the general formulas for the areas and the volumes of the solid figures. Correct formula and its substitution is the main step, do it wisely.