Question

एक खोखले बेलन की मोटाई 2सेमी है 'इसका भीतरी व्यास 14सेमी तथा ऊँचाई26सेमी है! खोखले बेलन का सम्पूर्ण पृष्ठीय क्षेत्र फल ज्ञात कीजिए

Answer 1

Given:

एक खोखले बेलन की मोटाई 2सेमी है 'इसका भीतरी व्यास 14सेमी तथा ऊँचाई26सेमी है!

If the width of the hollow cylinder is 2 cm its internal diameter is 14 cm and height 26 cm.

To find:

खोखले बेलन का सम्पूर्ण पृष्ठीय क्षेत्र फल ज्ञात कीजिए

The TSA of the cylinder

Solution:

The internal diameter = 14 cm

So, the internal radius, r = $\frac{14}{2}$ = 7 cm

The width of the hollow cylinder = 2 cm

∴ The external radius of the hollow cylinder, R = 7 + 2 = 9 cm

The height of the hollow cylinder, h = 26 cm

Therefore,

The total surface area of the hollow cylinder is,

= External surface area + Internal surface area + Base surface area

= $2\pi Rh + 2\pi rh + 2\pi(R^2 - r^2)$

= $2\pi h (R+ r) + 2\pi(R^2 - r^2)$

on substituting the values of R, r & h, we get

= $[2\times \frac{22}{7} \times 26 \times (9+ 7) ]+ [2\times \frac{22}{7} \times (9^2 - 7^2)]$

= $[2\times \frac{22}{7} \times 26 \times 16 ]+ [2\times \frac{22}{7} \times (81 - 49)]$

= $[2\times \frac{22}{7} \times 26 \times 16 ]+ [2\times \frac{22}{7} \times 32]$

= $2614.85 + 201.14$

= $2815.99\:cm^2$

≈ $\bold{2816\:cm^2}$

Thus, the total surface area of the hollow cylinder is → 2816 cm².

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