Question

the sum of the radius of the base and height of the solid right circular cylinder is 37 CM if its total surface area is 1628 centimetre square find its volume ​

Answer 1

Given ;

• Sum of radius of base and height of right circular cylinder is equal to 37 cm

• T.S.A ( Total Surface Area ) = 1628 cm²

Solution :-

Let Height be h & Radius = ( 37 - h ) cm

TSA of cylinder = 2πr ( h + r )

⟹ 1628 = 2π (37 - h) ( h + 37 - h)

⟹ (37)² - 37h = $\big \frac{\cancel{1628}{\:\:\:}^{\cancel{814}{\:\:\:}^{\cancel{407}{\:\:\:}^{37}{\:\:\:}}} \:\:\: \: \times 7}{\cancel2 \times \cancel{22}\: \: _{\cancel{11}}\:\:_1}$

⟹ $\rm\cancel{37}( 37 - h ) = \cancel{37} \times 7$

⟹ h = 37 - 7

$\therefore$ h = 30 cm

So,

Radius = ( 37 - h )cm [ h = 30 cm ]

⟹ ( 37 - 30 ) cm

$\therefore$ 7 cm

Volume of cylinder = $\bf \pi {r}^{2}h$

⟹ $\frac {22}{\cancel7} \times \cancel7 \times 7 \times 30$

$\rm\red{\therefore 4620 {cm}^{3}}$

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Another process :-

Given,

r + h = 37 cm

Total surface area = 1628 cm²

⟹ 2πr² + 2πrh = 1628 cm²

⟹ 2πr ( r + h ) = 1628 cm²

⟹ 2πr (37) = 1628 cm²

⟹ 2πr = $\large \rm\frac{\cancel{1628} {\:\:\:}{\cancel{cm} \times cm }{\:\:\:}^{44}}{\cancel{37cm}}$

⟹ 2 ( $\rm\frac{22}{7}r)$ = 44

⟹ r = 7 cm

Volume of cylinder = $\bf \pi {r}^{2}h$

⟹ $\frac {22}{\cancel7} \times \cancel7 \times 7 \times 30$

$\rm\red{ \therefore 4620 {cm}^{3}}$

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$\large \fbox \red {Hope \: it \: helps \: you}$