Question

contained
5. A wooden log of diameter 84 cm has a
length of 3.6 m. What is the volume of the
log? Express your answer in m?.​

Answer 1

Explanation:

length= 3.6 m

diameter= 84 cm

so, radius= 84/2= 42 cm= 0.42 m

$volume \: of \: cylinder = \pi {r}^{2} h$

therefore, volume= 1.99584 cubic m

Answer 2

Answer:

Volume of the wooden log is 1.99584 m³.

Explanation:

As per the provided information in the given question, we have :

• Diameter of the wooden log = 84 cm
• Length or height of the wooden log = 3.6 m

We area asked to find the volume of the wooden log.

Wooden logs are found in the shape of cylinder. Therefore, we'll be using volume of the cylinder formula to calculate its volume.

$\underline{\boxed{\sf{Volume_{(Cylinder)} = \pi r^2 h }}}$

Before substituting the values we need to calculate the radius and convert the dimensions into metre which are given in cm.

★ Finding radius :

Given that the diameter of the wooden log is 84 cm. We know that,

➝ Diameter = 2 × Radius

➝ $\sf \dfrac{Diameter}{2}$ = Radius

Substituting values,

➝ $\cancel{ \sf \dfrac{84}{2}}$ cm = Radius

➝ 42 cm = Radius

★ Conversion of units :

Since, we got rhe radius in centimetre, so we need to convert it into m.

➝ Radius = 42 cm

• 1 cm = $\sf \dfrac{1}{100}$ m

➝ Radius = $\sf \dfrac{42}{100}$ m

➝ Radius = 0.42 m

$\therefore$ Radius of the wooden log is 0.42 m.

★ Finding volume of the wooden log :

We know that,

$\longrightarrow\underline{\boxed{\sf{Volume_{(Cylinder)} = \pi r^2 h }}}$

$\longrightarrow \sf {Volume = \Bigg \lgroup \dfrac{22}{7} \times (0.42)^2 \times 3.6 \Bigg \rgroup \; m^3 }$

$\longrightarrow \sf {Volume = \Bigg \lgroup \dfrac{22}{7} \times 0.42\times 0.42 \times 3.6 \Bigg \rgroup \; m^3 }$

$\longrightarrow \sf {Volume= \Bigg \lgroup \dfrac{22}{\cancel{7}} \times \dfrac{\cancel{42}}{100} \times \dfrac{42}{100} \times \dfrac{36}{10} \Bigg \rgroup \; m^3 }$

$\longrightarrow \sf {Volume = \Bigg \lgroup 22 \times \dfrac{6}{100} \times \dfrac{42}{100} \times \dfrac{36}{10} \Bigg \rgroup \; m^3 }$

$\longrightarrow \sf {Volume = \Bigg \lgroup \dfrac{22 \times 6 \times 42 \times 36 }{100 \times 100 \times 10} \Bigg \rgroup \; m^3 }$

$\longrightarrow \sf {Volume = \Bigg \lgroup \dfrac{199584}{100000} \Bigg \rgroup \; m^3 }$

$\longrightarrow \underline{\boxed{ \sf {Volume_{(Wooden \; log)} = 1.99584 \; m^3 }}} \; \bigstar$

$\therefore$ Volume of the wooden log is 1.99584 m³.