Question

If the scale factor of two similar solids is 5:13, what is the ratio their corresponding areas and volumes?

Answer 1

@Michele_Laino Please help me!

Answer 2

@dan815 Please help me!

Answer 3

Let's suppose that your solids are two cubes, one whose edge is L_!, and the other whose edge is L_2. Then we can write:
\[\Large \frac{{L_1^3}}{{L_2^3}} = \frac{5}{{13}}\]
or:
\[\Large \frac{{L_1^{}}}{{L_2^{}}} = \sqrt[3]{{\frac{5}{{13}}}}\]

Answer 4

I think it is 25:169 and 125:2,197. Am i correct?

Answer 5

am i right?

Answer 6

or it is 125:2,197 and 25:169

Answer 7

no, I don't think, since the area of each cube is:
\[\Large \begin{gathered}
{S_1} = 6L_1^2 \hfill \\
{S_2} = 6L_2^2 \hfill \\
\end{gathered} \]
then their ratio is:
\[\Large \frac{{{S_1}}}{{{S_2}}} = \frac{{6L_1^2}}{{6L_2^2}} = \frac{{L_1^2}}{{L_2^2}} = {\left( {\frac{{L_1^{}}}{{L_2^{}}}} \right)^2} = {\left( {\sqrt[3]{{\frac{5}{{13}}}}} \right)^2} = {\left( {\frac{5}{{13}}} \right)^{2/3}}\]

Answer 8

is it 10:26 and 15:39
i get different answers every time

Answer 9

sorry I have ,ade an error, you are right since your problem says:
\[\Large \frac{{L_1^{}}}{{L_2^{}}} = \frac{5}{{13}}\]
so:
\[\Large \begin{gathered}
\frac{{{S_1}}}{{{S_2}}} = \frac{{6L_1^2}}{{6L_2^2}} = \frac{{L_1^2}}{{L_2^2}} = {\left( {\frac{{L_1^{}}}{{L_2^{}}}} \right)^2} = {\left( {\frac{5}{{13}}} \right)^2} \hfill \\
\frac{{{V_1}}}{{{V_2}}} = \frac{{L_1^3}}{{L_2^3}} = {\left( {\frac{5}{{13}}} \right)^3} \hfill \\
\end{gathered} \]

Answer 10

oops...I have made

Answer 11

so it is 10:26 and 15:39

Answer 12

no, it is as you write above, namely:
25:169 and 125:2,197.

Answer 13

Thanks. can you help with more please?

Answer 14

yes!

Answer 15

what is the scale factor of a cube with the volume of 343ft ^3 to a cube with volume 2,744ft .^3

Answer 16

i think the answer is 2:1

Answer 17

the requested scale factor, is given by the subsequent ratio:
\[\Large scale\;factor = \sqrt[3]{{\frac{{343}}{{2744}}}} = ...?\]

Answer 18

so you are right: it is 1:2

Answer 19

thanks. a few more?

Answer 20

yes!

Answer 21

the volume of a sphere is 3,000 pi m ^3. What is the surface area of the sphere to the nearest square meter?

Answer 22

the volume V of a sphere whose radius is R, is given by the subsequent formula:
\[\Large V = \frac{{4\pi }}{3}{R^3}\]

Answer 23

i think it's 1079 m ^2

Answer 24

so the radius is given by the inverse formula:
\[\Large R = \sqrt[3]{{\frac{{3V}}{{4\pi }}}}\]
and the surface is therefore:
\[\Large S = 4\pi {R^2} = 4\pi {\left( {\sqrt[3]{{\frac{{3V}}{{4\pi }}}}} \right)^2}\]

Answer 25

so its 2158?

Answer 26

so we have:better is 2157 meters^2

Answer 27

thanks. I have another one.

Answer 28

ok!

Answer 29

a spherical balloon has a circumference of 21 cm . What is the approximate surface area of the balloon to the nearest square cm.

Answer 30

i think it is 561 cm

Answer 31

I think that that circle is athe maximum circle, so the radius R of your balloon, is:
\[\Large R = \frac{{circumference}}{{2\pi }} = \frac{{21}}{{2\pi }}\]
then the requested surface, is:
\[\Large S = 4\pi {R^2} = 4\pi {\left( {\frac{{21}}{{2\pi }}} \right)^2} = ...?\]

Answer 32

okay so the answer is 346?

Answer 33

I got 144

Answer 34

i got 140...

Answer 35

ok! that's right!

Answer 36

thanks.

Answer 37

thanks!

Answer 38

find the surface area of the sphere with the given dimension leave your answer in in terms of pi. radius of 60 m

Answer 39

The requested surface S is:
\[\Large S = 4\pi {R^2} = 4\pi {\left( {60} \right)^2} = \pi \times 4 \times 3600 = ...?\]

Answer 40

14, 400 pi?

Answer 41

that's right!

Answer 42

thanks.

Answer 43

thanks!

Answer 44

a rectangular pyramid fits exactly on top of a rectangular prism

Answer 45

the prism has a length of 18cm width of 6 cm and height of 9 cm. the pyramid has a height of 15 cm . find the volume of the composite space figure.

Answer 46

please wait a moment, someone is calling me to the phone

Answer 47

okay

Answer 48

ok! here I am

Answer 49

okay

Answer 50

the volume of the prism is:
\[\Large {V_{prism}} = 18 \times 6 \times 9 = ...?\]
whereas the volume of pyramid is:
\[\Large {V_{pyramid}} = \frac{1}{3}18 \times 6 \times 15 = ...?\]

Answer 51

i think it is 1512 cm ^3?

Answer 52

that's right!

Answer 53

thanks. one more then i have to go

Answer 54

ok!

Answer 55

the lateral area of a cone is 574 pi cm ^2 , the radius is 29 cm. what is the slant height to the nearest tenth of a cm?

Answer 56

i think it is 12.6

Answer 57

the lateral surface S of a cone, is given by the subsequent formula:
\[S = \frac{1}{2} \times C \times h\]
where C is the circumference, and h is the slanted height, so:

Answer 58

6.3?

Answer 59

\[\begin{gathered}
S = \frac{1}{2} \times C \times h = \pi \times R \times h \hfill \\
\hfill \\
h = \frac{S}{{\pi R}} = \frac{{574}}{{29 \times \pi }} = ...? \hfill \\
\end{gathered} \]

Answer 60

9.9? i keep getting different answers..

Answer 61

I got 6.3 cm

Answer 62

that was my second answer.. but thank you so much . i will be back tonight for more help!

Answer 63

ok! Thank you!