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Cylindrical pencil holder

- Radius: [tex]$10 \, \text{cm}$[/tex]
- Height: [tex]$15 \, \text{cm}$[/tex]

Rectangular pencil holder

[tex]\[
\begin{array}{l}
\text{Length} = 10 \, \text{cm} \\
\text{Breadth} = 8 \, \text{cm} \\
\text{Height} = 15 \, \text{cm}
\end{array}
\][/tex]

Identify dimensions that are the same in both pencil holders.

- Height: [tex]$15 \, \text{cm}$[/tex]

Determine the volume of the cylindrical pencil holder.

[tex]\[
\begin{aligned}
V &= \pi r^2 h \\
&= 3.14 \times (10 \, \text{cm})^2 \times 15 \, \text{cm} \\
&= 4710 \, \text{cm}^3
\end{aligned}
\][/tex]

(Note: The second volume calculation appears to be incorrect and should be disregarded.)



Answer :

GinnyAnswer
Sure, let's break down the problem step by step.

### Step-by-Step Solution:

1. Identify the Dimensions:
- The problem involves a cylindrical pencil holder with:
- Radius [tex]\( r = 10 \)[/tex] cm
- Height [tex]\( h = 15 \)[/tex] cm

2. Recognize Relevant Formula:
- To find the volume ([tex]\(v\)[/tex]) of a cylinder, we use the formula:
[tex]\[ v = \pi r^2 h \][/tex]
where [tex]\( \pi \)[/tex] (pi) is approximately 3.14.

3. Substitute the Given Values:
- Place the values of [tex]\( r \)[/tex] and [tex]\( h \)[/tex] into the formula:
[tex]\[ v = \pi \times (10 \text{ cm})^2 \times 15 \text{ cm} \][/tex]
- Calculate the square of the radius:
[tex]\[ v = \pi \times (100 \text{ cm}^2) \times 15 \text{ cm} \][/tex]

4. Perform the Multiplication:
- Multiply 100 cm² by 15 cm:
[tex]\[ v = \pi \times 1500 \text{ cm}^3 \][/tex]
- Multiply this result by π (3.14):
[tex]\[ v = 3.14 \times 1500 \text{ cm}^3 \][/tex]

5. Calculate the Final Volume:
- Compute the final multiplication:
[tex]\[ v = 4710 \text{ cm}^3 \][/tex]

Therefore, the volume of the cylindrical pencil holder is [tex]\( 4710 \)[/tex] cm³.

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