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- Surface Areas and Volumes - Exercise 13.1
- Surface Areas and Volumes - Exercise 13.2
- Surface Areas and Volumes - Exercise 13.3
- Surface Areas and Volumes - Exercise 13.4
- Surface Areas and Volumes - Exercise 13.5
- Surface Areas and Volumes - Exercise 13.6
- Surface Areas and Volumes - Exercise 13.7
- Surface Areas and Volumes - Exercise 13.8
- Surface Areas and Volumes - Exercise 13.9

The diameter of the moon is approximately one-fourth of the diameter of the earth.

Find the ratio of their surface areas.

Answer:

If the diameter of the earth is said d, then the diameter of the moon will be d/4 (as per given statement)

Radius of earth = d/2

Radius of moon = ½ × d/4 = d/8

\begin{aligned} &\text { Ratio of their Surface areas }=\frac{4 \pi\left(\frac{d}{8}\right)^{2}}{4 \pi\left(\frac{d}{2}\right)^{2}}=4 / 64=1 / 16\\ &\text { The ratio between their surface areas is } 1: 16 \text { . } \end{aligned}

"hello students welcome to lido q a video
session
i am seth your math tutor and question
for today is the diameter of the moon is
approximately one-fourth of the diameter
of the earth
find the ratio of their surface areas if
the diameter of the earth is said to be
d
then the diameter of the moon will be d
upon 4
that is the meaning of our first
sentence in the question
so here if
diameter
of earth is d
then diameter of the moon
is d upon 4
now radius of the earth will be equal to
b upon 2
as we have considered diameter is d
radius will be half of the diameter
and hence you can say that the radius of
the moon is d
upon it
so it was the diameter of the moon as d
by four
so d upon four
upon 2 that is d upon
8
so now we have radius of the moon and
radius of the earth
surface area of the moon can be given by
4
pi r square that is radius of the moon
so here surface area formula write down
as a general
surface area of sphere
4 pi r square hence
if you take here surface area of moon
and surface area of
earth and then you find ratio then your
answer comes out to be like this
surface area
of
moon
divided by surface area
of earth that is our ratio
so for moon we have radius d by d by
eight
so d by eight square and for
earth we have radius d by two
hence we can now proceed further to find
ratio
so required ratio
that is ratio will be equal to
d by 8 square upon
d by 2 square
that is 4
upon 64
so ratio comes out to be 1 upon
this is the fraction you can convert
this fraction in ratio as
ratio is equal to 1 is to 16
so ratio between their surfaces area are
1 is to 16.
this is our required ratio if you have
any query you can drop down below
in our comment section and subscribe to
lido for more such q a
thank you for watching"

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