Question

Total surface area of a right circular cylinder is 1540 cm? If its height is four times the radius, then find
the volume of the cylinder,
​

Answer 1

Given

• Total Surface Area of a Right Circular Cylinder → 1540 cm²
• Height is four times the radius

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To Find

• The volume of the cylinder

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Solution

To find the volume of the cylinder it is essential to find the height and radius of the cylinder first.

Formula to find the Area of a Right Circular Cylinder → 2πr (r + h)

Area of the Given Right Circular Cylinder → 1540 cm²

Let the Radius be 'r'

Height → 4r

Now let's solve the below equation to find the radius and height.

2πr (r + 4r) = 1540

Step 1: Simplify the equation.

⇒ 2πr (r + 4r) = 1540

⇒ 2πr (5r) = 1540

⇒ 10πr² = 1540

Step 2: Divide 10 from both sides of the equation.

⇒ 10πr² ÷ 10 = 1540 ÷ 10

⇒ πr² = 154

Step 3: Multiply 7/22 to both sides of the equation.

⇒ $\dfrac{22}{7} \times r^{2} \times\dfrac{7}{22}= 154 \times \dfrac{7}{22}$

⇒ r² = 7 × 7

⇒ r² = 49

Step 4: Find square root of 49.

⇒ r² = 49

⇒ r = √49

⇒ r = 7

∴ The radius → r = 7

∴ The height → 4r = 4(7) = 28

Now let's find the volume of the cylinder.

Formula to find the Volume of Cylinder → πr²h

Volume of Given Cylinder ⇒ π × (7)² × 28

⇒ π × 49 × 28

⇒ $\dfrac{22}{7} \times 49 \times 28$

⇒ 22 × 7 × 28

⇒ 4312 cm³

∴ The volume of the cylinder is 4312 cm³

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Answer 2

Answer:

Given :-

• Total surface area of a right circular cylinder is 1540 cm². It's height is four times the radius.

To Find :-

• What is the volume of the cylinder.

Formula Used :-

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

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

where,

• r = Radius
• h = Height

Solution :-

Let, the radius of a right circular cylinder be r

Then, if height is four times the radius,

Height = 4r

Given :

• Total surface area = 1540 cm²
• Height = 4r

According to the question by using the formula we get,

↦ $\sf 2{\pi}r(r + 4r) =\: 1540$

↦ $\sf 2{\pi}r(5r) =\: 1540$

↦ $\sf 10{\pi}{r}^{2} =\: 1540$

↦ $\sf {r}^{2} =\: \dfrac{154\cancel{0} \times 7}{1\cancel{0} \times 22}$

↦ $\sf {r}^{2} =\: \dfrac{154 \times 7}{22}$

↦ $\sf {r}^{2} =\: \dfrac{\cancel{1078}}{\cancel{22}}$

↦ $\sf {r}^{2} =\: 49$

↦ $\sf r =\: \sqrt{49}$

➦ $\sf\bold{r =\: 7\: cm}$

Hence, the radius of a right circular cylinder is 7 cm.

And, the height is 4(7 cm) = 28 cm

Now, we have to find the volume of the cylinder,

Given :

• Radius = 7 cm
• Height = 28 cm

According to the question by using the formula we get,

⇒ $\sf Volume\: of\: Cylinder =\: \dfrac{22}{7} \times {(7)}^{2} \times 28$

⇒ $\sf Volume\: of\: Cylinder =\: \dfrac{22}{7} \times 49 \times 28$

⇒ $\sf Volume\: of\: Cylinder =\: \dfrac{22}{\cancel{7}} \times {\cancel{1372}}$

⇒ $\sf Volume\: of\: Cylinder =\: 22 \times 196$

➠ $\sf\bold{\pink{Volume\: of\: Cylinder =\: 4312\: {cm}^{3}}}$

$\therefore$ The volume of cylinder is 4312 cm³ .