Question

प्र.11 धातु की किसी घनाभकार प्लेट की लम्बाई, चौड़ाई और मोटाई क्रमशः 3.525 मी, 2.025
मी. एवं 1.05 सेमी. है। उचित सार्थक अंकों तक प्लेट का क्षेत्रफल एवं आयतन ज्ञात
कीजिए।​

Answer 1

Given:

धातु की किसी घनाभकार प्लेट की लम्बाई, चौड़ाई और मोटाई क्रमशः 3.525 मी, 2.025 मी. एवं 1.05 सेमी. है।

The length, breadth and thickness of a cuboidal metal plate are 3.525 m, 2.025 m and 1.05 cm respectively.

To find:

उचित सार्थक अंकों तक प्लेट का क्षेत्रफल एवं आयतन ज्ञात कीजिए।​

Give the area and volume of the sheet to correct significant figures.

Solution:

The dimensions of the cuboidal metal plate:

Length, l = 3.525 m

Breadth, b = 2.025 m

Height, h = 1.05 cm = 0.0105 m

We know,

$\boxed{\bold{Surface \:Area \:of\: a\:cuboid = 2[lb+ bh+hl]}}\\\\\boxed{\bold{Volume \:of\: a\:cuboid = l \times b \times h}}$

Finding the surface area:

∴ The total surface area of the cuboidal metal plate is,

= TSA of a cuboid

= $2[(3.525 \times 2.025)+ (2.025 \times 0.0105)+(0.0105 \times 3.525)]$

= $2[7.138+0.0212 +0.0370]$

= $2 \times 7.196$

= $14.3924\:m^2$

correcting it to the 3 significant digits

= $\boxed{\bold{14.3\:m^2}}$

Finding the volume:

∴ The volume of the cuboidal metal plate is,

= Volume of a cuboid

= $3.525 \times 2.025 \times 0.0105$

= $0.074950312\:m^3$

correcting it to the 3 significant digits

= $\boxed{\bold{0.0749\:m^3}}$

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