Question

A tanker is made by joining two hemispheres of radius 3.5m each to each of the ends of a cylinder having height 27m and radius 7m. Petrol from this completely filled tanker is transformed into hemispherical vessels of radius 1.75m. Find the number of hemispherical vessels.
WITH COMPLETE METHOD

Answer 1

Answer:

If the petrol from the completely filled tanker cylindrical in shape with hemisphere attached at both the ends is transformed into hemispherical vessels of radius 1.75m, then the number of hemispherical vessels required is 387.

Step-by-step explanation:

The given tanker is in the shape of a cylinder with two hemispheres attached at each of the ends of the cylinder.

Step 1:

The radius of the hemispheres = 3.5 m each

∴ The volume of both the hemispheres of the tanker is,

= 2 × [ π r³]

= 2 × [ × × (3.5)³]

= 179.67 m³

Step 2:

The height of the cylinder = 27 m

The radius of the cylinder = 7 m

∴ The volume of the cylindrical portion of the tanker is,

= π r² h

= × (7)² × 27

= 4158 m³

Step 3:

Therefore,

The total volume of the tanker is given by,

= [volume of both the hemispherical portions ] + [volume of the cylindrical portion]

= 179.67 m³ + 4158 m³

= 4337.67 m³

Step 4:

It is given that the petrol from the tanker is filled into hemispherical vessels each of radius 1.75 m

Therefore,

The volume of each of the hemispherical vessel is,

= π r³

= × × (1.75)³

= 11.22 m³

Step 5:

Thus,

The required no. of hemispherical vessels are given by,

= [total volume of the tanker] / [volume of each of the hemispherical vessel]

= [4337.67] / [11.22]

= 386.60

≈ 387 approximately

Step-by-step explanation:

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Answer 2

GiVeN : -

• Radius (r) of hemisphere = 3.5 m

• Height (h) of Cylinder = 27m

• Radius(R) of Cylinder = 7m

• Radius of Another Hemisphere =1.75m

To FiNd : -

• Number of Hemispherical vessels.

SoLuTiOn : -

We know that,

Volume of hemisphere =

$\implies \: \frac{2}{3} \pi \times {r}^{3}$

And

Volume of Cylinder =

$\implies \: \pi \times {r}^{2} h$

So,

Total volume of the figure is =

$\implies2 \times \frac{2}{3} \pi \times {r}^{3} + \pi \times {r}^{2} h \\ \\ \implies \: \frac{4}{3} \pi \times {r}^{3} + \pi \times {r}^{2} h \\ \\ \implies \: \frac{4}{3} \times \frac{22}{7} \times 3.5 \times 3.5 \times 3.5 + \frac{22}{7} \times 7 \times 7 \times 27 \\ \\ \implies \: \frac{3773}{21} + \frac{29106}{7} \\ \\ \implies \: 179.67 + 4158 \\ \\ \implies \: 4337.67 {m}^{3}$

Now,

Volume of another hemisphere =

$\implies \frac{2}{3} \pi \times {r}^{3} \\ \\ \implies \: \frac{2}{3} \times \frac{22}{7} \times 1.75 \times 1.75 \times 1.75 \\ \\ \implies \: \frac{235.8125}{21} = 11.23 {m}^{3}$

Volume of Figure = Volume of another hemisphere

So,

No of hemisphere = Volume of Figure/ Volume of hemisphere

$\implies \: \frac{4337.67}{11.23} = 386.6$

So,

Number of vessels = 386 or 387