Question

1) A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, give that 1 cm3 of iron has approximately 8 g mass. (Use π = 3.14)

Class - X Solve step by step

Answer 1

$\huge{\bf{\underline{\red{Solution :}}}}$

$\bold{\boxed{\bf{\green{Given :}}}}$

Case - 1) First Cylinder :

• Height of First Cylinder { $\bold{h_{1}}$ } = 220 cm
• Radius of First Cylinder {$\bold{r_{1}}$ } = $\bold{\frac{24}{2}} = \bold{ 12 \ cm }}$

Case - 2) Second Cylinder :

Height of Second Cylinder {$\bold{h_{2}}$ } = 60 cm

Radius of Second Cylinder {$\bold{r_{2}}$ } = 8 cm

Volume of Iron pole = Volume of First Cylinder + Volume of Second Cylinder

$\implies \bold{ \pi[ r_{1}]^{2} h_{1} + \pi [r_2}]^{2} h^{2}}$

So π From both side Common :

∴$\implies \bold{\pi ([ r_1]^{2} h_{1} + [ r_2]^{2} h_{2} )}$

Now Put the values :

$\implies \bold{ 3.14 ( 144 \times 220 + 64 \times 60 )}$

$\implies \bold{ ( 31680 + 3840)}$

$\implies \bold{ 3.14 \times 35520 \ cm^{3} }$..............1) Equation

[ We don't solve Volume of iron pole Because When we find the mass of pole then this value easily solve ]

Now given in this question that :

∵  [ 1 gram = $\bold{\frac{1}{1000}} kg$ ]

1 cm³ of iron has Approximately 8g  = $\bold{\frac{8}{1000} }$

∴ From First equation volume of iron pole help to find mass of pole :

∴ 3.14 ×  35520 cm³ of Iron has Approximately mass :

$\implies \bold{ 3.14 \times 35520 \times {\frac{8}{1000} }}$

$\implies \bold{3.14 \times 284.160}$

$\implies \bold{892.26 \ kg}$ (Answer)

Answer 2

Answer:

• The height of the larger pole (cylinder) is 220 cm.
• The radius of the larger pole (cylinder) is 24/2 = 12 cm.
• The height of the smaller pole (cylinder) is 60 cm.
• The radius of the smaller pole (cylinder) is 8 cm.
• 1 cm³ = 8 g mass of iron.

Here, to find the mass of the the pole, we need to find the volume of the the poles/cylinder.

Formula of Volume of cylinder = πr²h

• Finding the volume of larger cylinder/pole:-

➜ 3.14 × (12)² × 220

➜ 3.14 × 144 × 220

➜ 3.14 × 31,680 cm³

• Finding the volume of larger cylinder/pole:-

➜ 3.14 × (8)² × 60

➜ 3.14 × 64 × 60

➜ 3.14 × 3,840 cm³

• Total Volume of the pole (larger pole + smaller pole):-

➜ (3.14 × 31,680) + (3.14 × 3,840)

➜ 3.14 × (31,680 + 3,840)

➜ 3.14 × 35,520

➜ 111,532.8 cm³

• Finding the mass of the whole pole if 1 cm³ = 8 g of iron:-

➜ 111,532.8 × 8

➜ 892,262.4 gram

$\rule{200}2$