Question

a solid cylinder has total surface area of 462 CM square if its CSA is one third of its TSA find radius and height of cylinder
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Answer 1

A solid cylinder has total surface area of 462 cm^2. If its CSA is one third of its TSA. The radius = 7cm and

height of cylinder = 3.5 cm.

Stepwise explanation is given below:

- Total surface area of the cylinder (TSA)=462CM²

- Curved surface area=1/3 of Total surface area

=(1/3) (462)

= (462/3)

=154CM²

 - Area of each circle =(462 - 154)/2

=154CM²

πR²=154

R²= 154/π

R²=49

R=7 cm

2πRH=154

- By putting the value of R and π

H=154*7/22*7

H=3.5 cm

Volume=πR²H=(22/7)*(49)*(35/10)

Volume=539CM³

Answer 2

Given :

A solid cylinder has total surface area of 462 square cm

The curved surface area of cylinder = $\dfrac{1}{3}$ of total surface area

To Find :

The radius of the cylinder

The height of the cylinder

Solution :

Let The radius of the cylinder = r cm

Let The height of the cylinder = h cm

∵   Total surface area of cylinder = curved surface area + 2 π radius²

A/Q curved surface area of cylinder = $\dfrac{1}{3}$ of total surface area

So,   462 cm² = $\dfrac{1}{3}$ × 462 cm²  + 2 π r²

Or,   2 π r² =  462 cm² - $\dfrac{462}{3}$ cm²

Or,   2 × 3.14 ×  r² = 462 cm² - 154  cm²

Or,   2 × 3.14 ×  r² = 308

Or,   6.28 ×  r² = 308

Or,                r² =  $\dfrac{308}{6.28}$

Or,                 r² = 49

∴                    r = $\sqrt{49}$

i.e          radius = 7 cm

So, The radius of the cylinder = r = 7 cm

∵    curved surface   =  $\dfrac{1}{3}$ of total surface area

∵    curved surface   =  2 π r h

So,   2 π r h = $\dfrac{1}{3}$ × 462 cm²

putting the value of r

i.e       2 × 3.14 × 7 cm × h = $\dfrac{462}{3}$ cm²

Or,      43.96 cm × h = 154 cm²

∴                             h = $\dfrac{154}{43.96}$ cm

i.e                  height = 3.5 cm

So, The height of the cylinder = h = 3.5 cm

Hence, The radius of the cylinder is 7 cm  And  The height of the cylinder is 3.5 cm  Answer