Question

1.The radius and height of a cylinder is 6 cm and 9 cm respectively. If the radius becomes half and the height increases by 3 cm, which of these describes the new volume of the cylinder? *

1 The new volume will be half the original volume.

2The new volume will be twice the original volume.

3The new volume will be thrice the original volume.

4The new volume will be one-third the original volume.​

Answer 1

Answer:

3. The new volume will be thrice the original volume. ${\boxed{\green{\checkmark{}}}}$

Step-by-step explanation:

Question says that, A cylinder of radius 6cm and height 9cm. If the radius becomes ½ and the height increases by 3cm. What will be the change in the volume?

Step 1 :

Finding the volume of the cylinder :

Volume of a cylinder is given by :

→ πr²h

• r (radius) = 6cm (given)
• h (height) = 9cm. (given)

So,

Volume of the cylinder :

→ π × 6² × 9

→ π × 36 × 9

→ 324π

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Step 2 :

Finding the volume of the new cylinder :

Here, the radius will be half by now :

→ ½ of ‘r’

→ ½ × 6

→ 3cm.

Similarly, the height increases by 3 :

→ h + 3

→ 9 + 3

→ 12cm.

Volume of the new cylinder :

→ πr²h

→ π × 3² × 12

→ π × 9 × 12

→ 108π

________________________________

Step 3 :

Calculating the change in the volumes :

The change in the volume is given by :

→ $\sf \frac{V_2}{V_1}$

Here, $\sf {V_1}{}$ is the volume of the original cylinder. And also, $\sf {V_2}{}$ refers to the volume of the new cylinder.

So,

→ $\sf \frac{V_2}{V_1}$

→ $\sf \frac{324 \pi}{108 \pi}$

→ ${\textsf{\textbf{3}}}$

∴ The new volume will be thrice the original volume.

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Answer 2

${\huge {\textsf {\textbf{ \color{plum}{Answer}}}}}$

3. The new volume will be thrice the original volume. ${\boxed{\red{\checkmark{}}}}$

$\large{ \textsf{ \textbf{ \orange{Step-by-step explanation :}}}}$

$\large\mathfrak{ \color{navy}{Step 1 :}}$

Finding the volume of the cylinder :

Volume of a cylinder is given by :

→ πr²h

• r (radius) = 6cm (given)
• h (height) = 9cm. (given)

So,

Volume of the cylinder :

→ π × 6² × 9

→ π × 36 × 9

→ 324π

_____________________

$\large\mathfrak{ \color{navy}{Step 2 :}}$

Finding the volume of the new cylinder :

Here, the radius will be half by now :

→ ½ of ‘r’

→ ½ × 6

→ 3cm

Similarly, the height increases by 3 :

→ h + 3

→ 9 + 3

→ 12cm

Volume of the new cylinder :

→ πr²h

→ π × 3² × 12

→ π × 9 × 12

→ 108π

_____________________

$\large \mathfrak{ \color{navy}{Step 3 :}}$

Calculating the change in the volumes :

The change in the volume is given by :

→ $\sf \frac{V_2}{V_1}$

Here, $\sf {V_1}{}$ is the volume of the original cylinder. And also, $\sf {V_2}{}$ refers to the volume of the new cylinder.

So,

→ $\sf \frac{V_2}{V_1}$

→ $\sf \frac{324 \pi}{108 \pi}$

→ ${\textsf{\textbf{3}}}$

∴ The new volume will be thrice the original volume.

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