Question

the circumference of the base of a cylindrical object is 2.2 m and height 40 cm, find the area of the total surface of the object.​

Answer 1

Required Answer :-

Given :-

• Circumference of base of cylindrical object is 2.2 m
• Height of cylindrical object (h) = 40 cm

To Find :-

• Total surface area of the cylindrical object?

Solution :-

We know that 1 m = 100 cm so circumference in cm will be; 2.2 × 100 = 220 cm

We know that base of cylinder is circular in shape and we know circumference of base so let's find radius of base (r) by using formula of circumference of circle.

We know that,

$\star\:{\boxed{\sf{Circumference_{(circle)} = 2\pi r}}}$

Putting all values,

$\\ \longrightarrow\:\sf 220 = 2\:\ast\:\dfrac{22}{7}\:\ast\:r$

$\\ \longrightarrow\:\sf 220 = \dfrac{2\:\ast\:22}{7}\:\ast\:r$

$\\ \longrightarrow\:\sf 220 = \dfrac{44}{7}\:\ast\:r$

$\\ \longrightarrow\:\sf \dfrac{44}{7}\:\ast\:r = 220$

$\\ \longrightarrow\:\sf r = 220\:\div\:\dfrac{44}{7}$

$\\ \longrightarrow\:\sf r = \cancel{220}\:\ast\:\dfrac{7}{\cancel{44}}$

$\\ \longrightarrow\:\sf r = 5\:\ast\:7$

$\\ \longrightarrow\:\underline{\underline{\sf{r = 35\:cm}}}$

Hence, radius of base of cylindrical object is 35 cm.

Now finding total surface area of cylinder by using formula of TSA of cylinder.

We know that,

$\star\:{\boxed{\sf{TSA_{(cylinder)} = 2\pi r\big(r + h\big)}}}$

Putting all values,

$\\ \longrightarrow\:\sf TSA_{(cylinder)} = 2\:\ast\:\dfrac{22}{\cancel{7}}\:\ast\:\cancel{35}\:\ast\:\big(35 + 40\big)$

$\\ \longrightarrow\:\sf TSA_{(cylinder)} = 2\:\ast\:22\:\ast\:5\:\ast\:75$

$\\ \longrightarrow\:\sf TSA_{(cylinder)} = 44\:\ast\:375$

$\\ \longrightarrow\:\underline{\underline{\sf{TSA_{(cylinder)} = 16500\:cm^2}}}$

Hence, area of total surface of cylindrical object is 16500 cm².

Important Formulae :-

↠ TSA of cube = 6a²

↠ CSA of cube = 4a²

↠ Volume of cube = a³

↠ TSA of cuboid = 2(lb + bh + hl)

↠ CSA of cuboid = 2(l + b)h

↠ Volume of cuboid = l × b × h

↠ TSA of cylinder = 2πr(r + h)

↠ CSA of cylinder = 2πrh

↠ Volume of cylinder = πr²h

↠ Volume of hollow cylinder = πh(R²-r²)

↠ TSA of cone = πr(l + r)

↠ CSA of cone = πrl

↠ Volume of cone = 1/3πr²h

↠ SA of sphere = 4πr²

↠ Volume of sphere = 4/3πr³

↠ TSA of hemisphere = 3πr²

↠ CSA of hemisphere = 2πr²

↠ Volume of hemisphere = 2/3πr³

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