Question

a log of wood in the shape of cylinder has length 2m and diameter 70cm .find the volume of wood log $(pi =22/7)$

Answer 1

Required Answer:

Given:

• A log of wood is in cylindrical shape.

• Length of wood = 2 m.

• Diameter of its base = 70 cm

To calculate:

• Volume of the log of wood.

Calculation:

Here, let us first convert the given quantities in same units i.e either in m or cm.

We can also says its length as its height.

Now, performing conversion:

• Length or height = 2 m = 200 cm

→ 1 m = 100 cm

→ 2 m = ( 2 × 100 ) cm

→ 2 m = 200 cm

• Diameter = 70 cm

Now, here we'll apply the formula of volume. As we know that,

★ $\boxed{\sf{{Volume}_{(Cylinder)} = \pi {r}^{2} h}}$

So, before substituting values, let's find the radius of its base:

→ Diameter = 70 cm ⠀⠀⠀⠀⠀⠀⠀⠀⠀[Given]

→ Diameter = 2 × Radius

→ $\sf{\dfrac{Diameter}{2}}$ = Radius

→ $\sf{\dfrac{70}{2}}$ = Radius

→ 35 cm = Radius

Inserting values, we get:

→ Volume = [ $\sf{\dfrac{22}{7}}$ × (35)² × 200 ] cm³

→ Volume = [ $\sf{\dfrac{22}{7}}$ × 35 × 35 × 200 ] cm³

→ Volume = [ 22 × 5 × 35 × 200 ] cm³

→ Volume = 770,000 cm³

Hence,the volume of wood log is 770,000 cm³.

Answer 2

The wood is in the shape of a right circular cylineder where,

$\boxed{ V = \pi r^2 h}$.

Give that, d = 70 cm ⇒ r = 35 cm

(∵ d = 2r)

Height = 2 m or 200 cm

∴ V = π(35 cm)(35 cm)(200 cm)

⇒ V = (22/7)(35)(35)(200) cm³

⇒ V = 22 × 5 × 35 × 200 cm³

⇒ V = 770000 cm³ or 0.77 m³ (ans.)

More:-

• TSA = $2 \pi r(r + h)$
• CSA = $2 \pi r h$
• Thickness = $(R - r)$.
• Volume of hollow cylinder = $\pi h (R + r)(R - r)$.
• If (R + r) and (R - r) is given, then subtract of add (R - r) and (R + r) equation to get either R (by adding) or r (by subtracting) to get the value of ext. and int. radii.