Video Transcript
Daniel and Charlotte both have
a keen interest in gardening and are concerned by the number of slugs that they
keep finding in their respective vegetable patches. They want to compare the number
of slugs in each of their gardens. But due to the differences in
size of their vegetable patches, they decide to compare the number of slugs per
square foot. Daniel’s vegetable patch is a
rectangle with dimensions five foot by three foot. And Charlotte’s is a circular
patch with a radius of three foot. One Saturday morning, Daniel
counts 21 slugs in his entire vegetable patch and Charlotte counts 36. There are three parts to this
question. Work out the density of slugs
in Daniel’s vegetable patch. Work out the density of slugs
in Charlotte’s vegetable patch. Who has the more severe slug
problem?
We’re told that Daniel’s patch
is rectangular and measures five foot by three foot, whereas Charlotte’s is
circular with a radius of three foot. There were 21 slugs in Daniel’s
vegetable patch and 36 in Charlotte’s. We will now clear some space to
calculate the number of slugs they had per square foot. Let’s consider Daniel’s
vegetable patch first. His patch was rectangular with
dimensions three foot and five foot, and he found 21 slugs in his patch. We can calculate the area of
any rectangle by multiplying the length by the width. In this case, we need to
multiply five by three. This is equal to 15. Therefore, Daniel’s patch has
an area of 15 square foot.
In order to calculate the
density per square foot, we can, firstly, write the ratio of the area to the
number of slugs. This is equal to 15 to 21. To calculate the density of
slugs in Daniel’s patch, we need to calculate the unit ratio, how many slugs
there are per square foot. This is written in the form one
to 𝑛. We divide both sides of the
ratio by 15, giving us the ratio one to 1.4. The density of slugs in
Daniel’s vegetable patch is therefore 1.4 slugs per square foot.
We can now repeat this process
for Charlotte.
Charlotte’s vegetable patch was
circular and had a
ratio
[radius] of three foot.
She found 36 slugs in her
vegetable patch. The area of any circle can be
calculated by multiplying 𝜋 by the radius squared. In this question, this is equal
to 𝜋 multiplied by three squared. This is equal to 28.2743 and so
on. This means that the area of
Charlotte’s vegetable patch is 28.27 square feet. For the purposes of this
question, we will keep this as nine 𝜋. The ratio of area to slugs for
Charlotte is therefore nine 𝜋 to 36. To find the unit ratio or
density, we can divide both sides by nine 𝜋. 36 divided by nine 𝜋 is equal
to 1.273 and so on. Rounding this to one decimal
place gives us 1.3 slugs per square foot.
The three correct answers are
1.4, 1.3, and Daniel. As 1.4 is greater than 1.3,
Daniel has the more severe slug problem.
