Question

If the volume of cylinder is 770 cu. cm and height is 5 cm. Then find the TSA of volume.

Answer 1

Answer:

volume = πr²h

770 = 22/7 × r × r × 5

770 × 7/22 × 5 = r²

49 = r²

r = √49 = √7 × 7 = 7cm

7cm is the radius.

TSA = 2πr ( r + h )

TSA = 2 × 22/7 × 7 × ( 7 + 5 )

TSA = 2 × 22/7 × 7 × 12

TSA = 528cm²

Answer 2

Answer:

Given :-

• The volume of cylinder is 770 cm³ and the height is 5 cm.

To Find :-

• What is the TSA or total surface area of a cylinder.

Formula Used :-

$\sf\boxed{\bold{Volume\: of\: Cylinder =\: {\pi}{r}^{2}h}}$

$\sf\boxed{\bold{T.S.A\: of\: Cylinder =\: 2{\pi}r(r + h)}}$

where,

• r = Radius
• h = Height
• T.S.A = Total surface area

Solution :-

First, we have to find the radius of a cylinder :

Given :

• Height = 5 cm

According to the question by using the formula we have,

↦ $\sf \dfrac{22}{7} \times {r}^{2} \times 5 =\: 770$

↦ $\sf {r}^{2} =\: \dfrac{770 \times 7}{22 \times 5}$

↦ $\sf {r}^{2} =\: \dfrac{\cancel{5390}}{\cancel{110}}$

↦ $\sf {r}^{2} =\: 49$

↦ $\sf r =\: \sqrt{49}$

➦ $\sf\bold{\pink{r =\: 7\: cm}}$

Hence, the radius of a cylinder is 7 cm.

Now, we have to find the total surface area of a cylinder,

Given :

• Radius = 7 cm
• Height = 5 cm

According to the question by using the formula we get,

$\implies \sf T.S.A\: of\: Cylinder =\: 2 \times \dfrac{22}{\cancel{7}} \times {\cancel{7}}(7 + 5)$

$\implies \sf T.S.A\: of\: Cylinder =\: 2 \times 22(12)$

$\implies \sf T.S.A\: of\: Cylinder =\: 44 \times 12$

$\implies \sf\bold{\red{T.S.A\: of\: Cylinder =\: 528\: {cm}^{2}}}$

$\therefore$ The total surface area or T.S.A of cylinder is 528 cm².