Question

Two solids of cylindrical shape are 49cm and 35cm high and base
diameters 16cm and 14cm are melted and recast into new cylinder.
Find the volume of the new cylinder formed

Answer 1

Given -

• Height of 1st cylinder = 49cm

• Diameter of 1st cylinder = 16cm

• Radius of 1st cylinder = 16/2 = 8cm

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• Height of 2nd cylinder = 35cm

• Diameter of 2nd cylinder = 14cm

• Radius of 2nd cylinder = 14/2 = 7cm

To find -

• Volume of the new cylinder formed.

Solution -

Let's find the volume of both the cylinders.

Volume of 1st cylinder = πr²h

Where,

π = 22/7

r = Radius

h = Height

On substituting the values -

Volume = πr²h

Volume = 22/7 × 8 × 8 × 49

Volume = 9856cm³

Volume of 2nd cylinder - πr²h

Volume = 22/7 × 7 × 7 × 35

Volume = 22 × 7 × 7 × 5

Volume = 5390cm³

Now,

Volume of new cylinder formed = volume of 1st cylinder + Volume of 2nd cylinder

Volume = 9856 + 5390 cm³

Volume = 15246cm³

$\therefore$ The Volume of the new cylinder formed is 15246cm³

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Answer 2

Answer:

Given :-

• Two solids of cylindrical shape are 49 cm and 35 cm high and base diameter are 16 cm and 14 cm are melted and recast into new cylinder.

To Find :-

• What is the volume of the new cylinder formed.

Formula Used :-

$\boxed{\bold{\large{Volume\: of\: cylinder\: =\: {\pi}{r}^{2}h}}}$

where,

• r = Radius
• h = Height

Solution :-

❖ For the 1st cylinder,

Given :

• Height = 49 cm
• Diameter = 16 cm

First, we have to find the radius,

We know that,

Radius = $\dfrac{Diameter}{2}$

⇒ Radius = $\dfrac{16}{8}$

➠ Radius = 8 cm

Now, we have to find the volume of 1st cylinder,

According to the question by using the formula we get,

➟ Volume = $\dfrac{22}{7} \times (8)² \times 49$

➟ Volume = $\dfrac{22}{7} \times 64 \times 49$

➟ Volume = $\dfrac{22}{7} \times 3136$

➥ Volume = 9856 cm³

Hence, the volume of 1st cylinder is 9856 cm³ .

❖ For the 2nd cylinder,

Given :

• Height = 35 cm
• Diameter = 14 cm

First, we have to find the radius,

⇒ Radius = $\dfrac{14}{2}$

➠ Radius = 7 cm

Now, we have to find the volume of 2nd cylinder,

According to the question by using the formula we get,

↦ Volume = $\dfrac{22}{7} \times (7)² \times 35$

↦ Volume = $\dfrac{22}{7} \times 49 \times 35$

↦ Volume = $\dfrac{22}{7} \times 1715$

➠ Volume = 5390 cm³

Hence, the volume of 2nd cylinder is 5390 cm³ .

Now, we have to find the volume of new cylinder,

✪ Volume of new cylinder = Volume of 1st cylinder + Volume of 2nd cylinder ✪

According to the question by using the formula we get,

➙ Volume of new cylinder = 9856 + 5390

➣ Volume of new cylinder = 15246 cm³

$\therefore$ The volume of new cylinder formed is 15246 cm³ .