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3 years ago

yuri has a rope 12 meters long. he cuts it into pieces that are each 2 meters long. what fraction of the rope is one piece

Mathematics

2 answers:

melamori03 [73]3 years ago

8 0

2/12
1/6
it's either the first one or the second one they r the same

Juli2301 [7.4K]3 years ago

7 0

The answer is $\dfrac{1}{6}$ .

The rope is 12 meters long and each piece cut out is 2 meters long.

So we know that each piece measures 2 meters out of the 12 meters. With this alone we can make a fraction:

2 out of 12:

$\dfrac{2}{12}$

This can be simplified further by dividing the numerator and denominator by 2.

$\dfrac{2\div 2}{12\div2} = \dfrac {1}{6}$

Each piece is one-sixth of the rope.

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Step 1:

We will calculate the volume of ice cream in the single scoop

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$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}$

By substituting the values, we will have

$\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}$

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}$

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}$

For the first ice cream with one scoop