Question

The total surface area of a solid cylinder is 968 cm sq. If curved surface area of the cylinder is 660 cm sq. find the height and volume of the cylinder.​

Answer 1

➠ Height of cylinder = 15 cm.

➠ Volume of cylinder = 2310 cm².

Step-by-step explanation:

★ Given that :

• Total surface area of Cylinder : 968 cm².
• Curved surface area of Cylinder : 660 cm².

★ To find :

• Height of cylinder.
• Volume of cylinder.

★ Formula :

$\boxed{\large{\tt{\gray{\underline{\blue{Curved\:surface\:area_{(Cylinder)} = 2\pi rh}}}}}}$

$\sf \implies 2 \times \cfrac{22} {7} \times rh = 660$

$\sf \implies rh = \cancel{660} \times \cfrac{7}{\cancel{22}} \times \cfrac{1}{\cancel{2}}$

$\sf \implies rh = 105 .....(1)$

$\boxed{\large{ \tt{\gray{\underline{\blue{ Total\:surface\:area_{(Cylinder)} = 2\pi r(r + h)}}}}}}$

$\sf \implies 2 \times \cfrac{22}{7} \times r(r + h) = 968$

$\sf \implies r^{2} + rh = \cancel{968} \times \cfrac{7}{\cancel{22}} \times \cfrac{1}{\cancel{2}}$

$\sf \implies r^{2} + rh = 154$

• Substitute value of (1).

$\sf \implies r^{2} + 105 = 154$

$\sf \implies r^{2} = 154 - 105$

$\sf \implies r^{2} = 49$

$\sf \implies r= \sqrt{49}$

$\sf \implies r= 7$

• Substitute value of radius in (1).

$\sf \implies 7h = 105$

$\sf \implies h = \cfrac{\cancel{105}}{\cancel{7}}$

$\sf \implies h = 15$

★ Verification :

Substitute the values of radius and height of cylinder in CSA formula.

$\sf \implies CSA_{(Cylinder)} = 2\pi rh$

$\sf \implies CSA_{(Cylinder)} = 2\times \cfrac{22}{\cancel{7}}\times \cancel{7} \times 15$

$\sf \implies CSA_{(Cylinder)} = 660$

Since, CSA of Cylinder = 660 cm².

Hence, it was verified.

★ Now :

Find out the value of volume of cylinder.

$\boxed{\large{ \tt{\gray{\underline{\blue{ Volume_{(Cylinder)} = \pi r^{2}h}}}}}}$

$\sf \implies \cfrac{22}{\cancel{7}} \cancel{\times 7} \times 7 \times 15$

$\sf \implies 2310$

$\underline{\boxed{\rm{\purple{\therefore Height_{(Cylinder)} = 15\:cm.}}}}\:\orange{\bigstar}$

$\underline{\boxed{\rm{\purple{\therefore Volume_{(Cylinder)} = 2310\:cm^{2}.}}}}\:\orange{\bigstar}$

★ More info :

Formula related to Cylinders :

◼ TSA = 2πr(r + h)

◼ CSA = 2πrh

◼ Volume = πr²h

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