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3 years ago

11

Mark uses an app that shows him how many kilometers he has run to prepare for a marathon. The app said he ran 9.654 kilometers.

He wants to post online how many miles he ran. Mark ran ___ miles. (1 mile = 1.609 kilometers)

2 answers:

svetlana [45]3 years ago

8 0

Mark would have ran 6 miles if he ran 9.654 kilometers

AfilCa [17]3 years ago

5 0

1 mile = 1.609 km
so 9.654 km = 9.654/1.609 miles
so he ran 6 miles

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Answer:

16 times

Step-by-step explanation:

$\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.

$\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h$

Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so <u>16 times greater </u>than the smaller cone.

<h3><u>Proof</u></h3>

Given:

radius = 6
height = 9

Substituting the given values into the formula:

$\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units$

If the radius is quadrupled:

radius = 6 × 4 = 24
height = 9

Substituting the new given values into the formula:

$\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units$

To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:

$\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16$

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