Question

The inner and outer walls of a 30 cm long pipe have a diameter of 15 cm and 17 cm, respectively. Find the volume of the material used in the pipe (use π = 3.14). ​

Answer 1

Answer:

The volume of material used in the pipe is 1507.2 cm³.

Step-by-step explanation:

As per the provided information in the question, we have :

• ➛ Height of wall = 30 cm
• ➛ Diameter of inner wall = 15 cm
• ➛ Diameter of outer wall = 17 cm
• ➛ Radius of inner wall = 15/2 = 7.5 cm
• ➛ Radius of outer wall = 17/2 = 8.5 cm

Here's the required formula to find the volume of material used in the pipe :

$\quad{\longrightarrow{\pmb{\sf{ V = \pi h\Big(Outer}^{2} - {Inner}^{2}\Big)}}}$

• ↝ V = Volume
• ↝ π = 3.14
• ↝ h = height
• ↝ Outer = Outer radius
• ↝ Inner = Inner radius

Substituting all the given values in the formula to find the volume of material used in the pipe :

$\quad{\twoheadrightarrow{\sf{ V =\pi h\Big({Outer}^{2} - {Inner}^{2}\Big)}}}$

$\quad{\twoheadrightarrow{\sf{ V =3.14 \times 30\Big({(8.5)}^{2} - {(7.5)}^{2}\Big)}}}$

$\quad{\twoheadrightarrow{\sf{ V =94.2\Big((8.5 \times 8.5) - (7.5 \times 7.5)\Big)}}}$

$\quad{\twoheadrightarrow{\sf{ V =94.2\Big((72.25) - (56.25)\Big)}}}$

$\quad{\twoheadrightarrow{\sf{ V =94.2\Big(72.25 - 56.25\Big)}}}$

$\quad{\twoheadrightarrow{\sf{ V =94.2\Big( \: 16 \: \Big)}}}$

$\quad{\twoheadrightarrow{\sf{ V =94.2 \times 16}}}$

$\quad{\twoheadrightarrow{\sf{ V =1507.2}}}$

$\quad\star{\underline{\boxed{\sf{\red{ V =1507.2 \: {cm}^{3}}}}}}$

Hence, the volume of material used in the pipe is 1507.2 cm³.

$\rule{300}{2.5}$

Answer 2

The volume of the material used is 1507.2cm^3

Data;

• height = 30cm
• inner diameter = 15cm; radius = 7.5cm
• outer diameter = 17cm; radius = 8.5cm
• π = 3.14

Volume of a Cylinder

The formula of volume of a cylinder is given as

$v = \pi r^2 h$

But in this case, we have to find the difference between the outer radius and the inner radius.

$v = \pi h(r_2^2 - r_1^2)$

Let's substitute the values and solve.

$V = 3.14 * 30 * (8.5^2 - 7.5^2)\\v = 94.2 * (16\\v = 94.2 * 16\\v = 1507.2cm^3$

The volume of the material used is 1507.2cm^3

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