Mathematics: Find the height of a cylinder whose radius is 7cm and Total Surface Area is 968cm2 with steps

2.75 + .003 + .158 =2.753+.158 = 2.911...

Find the height of a cylinder whose radius is 7cm

dondre54

26.12.2021

The height of cylinder is 15 cm.

Step-by-step explanation:

Given :

✧ Radius of cylinder = 7cm✧ Total surface area = 968cm²

To Find :

✧ Height of cylinder

Using Formula :

${\star{\small{ \underline{ \boxed{\sf{\red{TSA_{(Cylinder)} = 2\pi r(r + h)}}}}}}}$

✧ Tsa = Total surface area ✧ π = 22/7✧ r = radius ✧ h = height

Solution :

Substituting all the given values in the formula to find height of cylinder :

${\longrightarrow{\small{\sf{ \: TSA_{(Cylinder)} = 2\pi r(r + h)}}}}$

${\longrightarrow{\small{\sf{ \: 968= 2 \times \dfrac{22}{7} \times 7(7 + h)}}}}$

${\longrightarrow{\small{\sf{ \: 968= 2 \times \dfrac{22}{\cancel{7}} \times \cancel{7}(7 + h)}}}}$

${\longrightarrow{\small{\sf{ \: 968= 2 \times 22(7 + h)}}}}$

${\longrightarrow{\small{\sf{ \: 968= 44(7 + h)}}}}$

${\longrightarrow{\small{\sf{ \: (7 + h) = \dfrac{968}{44}}}}}$

${\longrightarrow{\small{\sf{ \: (7 + h) = \cancel{\dfrac{968}{44}}}}}}$

${\longrightarrow{\small{\sf{ \: (7 + h) = 22}}}}$

${\longrightarrow{\small{\sf{ \: 7 + h = 22}}}}$

${\longrightarrow{\small{\sf{ \: h = 22 - 7}}}}$

${\longrightarrow{\small{\sf{ \: h = 15 \: cm}}}}$

${\star{\small{ \underline{ \boxed{\sf{\red{Height = 15cm}}}}}}}$

Hence, the height of cylinder is 15 cm.

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