Question

the radius and height of a cylinder are in the ratio 7ratio2.if volume is 8316 cm³find total surface area​

Answer 1

Given :

• Volume of a cylinder = 8316³
• Radius and height of the cylinder are in the ratio = 7:2

To find :

• The total surface area of a cylinder

According to the question,

Let,

• The radius of a cylinder be 7x
• The height of a cylinder be 2x

We know,

➞ Volume of cylinder = πr²h

$\sf : \implies{Volume \: of \: cylinder = \pi {r}^{2} h}$

$\sf : \implies{ {8316 \: cm}^{3} = \dfrac{22}{7} \times 7x \times 7x \times 2x }$

$\sf : \implies{8316 {cm}^{3} = 22 \times x \times 14{x}^{2} }$

$\sf : \implies{8316 \: {cm}^{3} = 308 {x}^{3} }$

$\sf : \implies{ \dfrac{8316}{308} \: {cm}^{3} = {x}^{3} }$

$\sf: \implies{27 \: {cm}^{3} = {x}^{3} }$

$\sf : \implies{ \sqrt{27 \: {cm}^{3} } = x }$

${ \underline{ \boxed{\bf \red{: \implies{3 \: cm = x}}}} }\: \bigstar$

So,

• The radius is = 7x = 7 × 3 ➞ 21 cm
• The height is = 2x = 2 × 3 ➞ 6 cm

Now,

➞ Total surface area of a cylinder = 2πr(r + h)

$\sf : \implies{Total \: surface \: area \: of \: a \: cylinder = 2 \pi r(r + h)}$

$\sf : \implies{2 \times \dfrac{22}{7} \times 21 \: cm \times(21 \: cm + 6 \: cm) }$

$\sf : \implies{44 \times 3 \: cm \times 27 \: cm}$

${ \underline{ \boxed{ \bf \pink{ : \implies{3564 \: {cm}^{2} }}}}} \: \bigstar$

$\therefore\underline{ \sf{So, the \: total \: surface \: area \: of \: a \: cylinder \: is \: 3564 {cm}^{2} }}$

Answer 2

Answer:

Given :-

• Volume of a cylinder = 8316³
• Radius and height of the cylinder are in the ratio = 7:2

To Find :-

TSA

Solution :-

As we know that

Volume = πr²

Let the ratio be 7x and 2x

8316 = 22/7 × 7x × 7x × 2x

8316 = 22 × x × 14x²

8316 = 308x ³

8316/308 = x³

27 cm = x³

x = ³√27

x = 3

The radius = 7x = 7 × 3 ➞ 21 cm

The height = 2x = 2 × 3 ➞ 6 cm

Now,

Let's find TSA

TSA of Cylinder = 2πr(r + h)

TSA = 2 × 22/7 × 21 (21+6)

TSA = 2 × 22 × 3(27)

TSA = 3564 cm³

$\rule{90}{1}$