Question

6. If the lateral area of a right circular cylinder is 9m^2 and its volume is 27m^3, find its diameter.

Answer 1

Can you answer this problem?

Answer 2

Plese note that if I call A as the lateral area of your right circular cylinder, and V its volume, I can write:
\[A=2 \pi *r*h\]
and:
\[V=\pi*r ^{2}*h\]
where h is the height of your cylinder and r is its radius. Now substituting your numerica data in the above equations, I get:
\[2 \pi*r*h=9\]
and:
\[\pi*r ^{2}*h=27\]
So you have to solve those pair of equations, namely a system of two equations in two variable. DO you know how to solve it, please?

Answer 3

I dont know how..

Answer 4

Its not clear to me yet.

Answer 5

Oh! I got the answer already

Answer 6

Ok! I help you to solve it. Please solve first equation in order to find h, namely you have to divide both sides of the first equation by 2*pi*r, please try now

Answer 7

I now got the answer. The radius is 6 and the diameter is 12.

Answer 8

that's right!

Answer 9

Thank you!

Answer 10

thank you!

Answer 11

A right circular cone is inscribed in a cube whose diagonal measures 8sqrtof3cm. Find the volume of the cone.

Answer 12

Can u answer this please?

Answer 13

yes!

Answer 14

If I call l the edge of your cube, and d its diagonal, then applyng twice the Pitagora theorem, I get:
\[d=l*\sqrt{3}\]
or squaring both sides:
\[d ^{2}=3*l ^{2}\]
Now substituting your numerical dat, I find:
\[l=2\sqrt{2}\]
Radius R of your cone is equal to l/2, so:
\[R=\sqrt{2}\]
height H of your cone is:
\[H=l=2\sqrt{2}\]
Finally applying the formula to find the volume of a cone, we can write:
\[V=\frac{ 1 }{ 3 }\pi*R^{2}*H=\frac{ \pi }{ 3 }*2*2\sqrt{2}=\frac{ 4 \pi }{ 3 }\sqrt{2}\]

Answer 15

@Paulaaquino please, check all of my statements!

Answer 16

I got the volume already. and its 134.04 but i used another solution (;

Answer 17

you are right, I have made an error, sorry, I write all corrections.
whit same meaning of symbols, I write:
\[l=8, R=4V=\frac{ 1 }{ 3 }*\pi 16*8\]
check this, I think it is correct!

Answer 18

@Paulaaquino is it correct?

Answer 19

Yes :)

Answer 20

Its okay, we are all persons we make mistakes :)

Answer 21

9. The base of the right prism is a regular pentagon with one side measuring 12cm. find the volume and the total surface area of the altitude measures 48 cm.

Answer 22

thank you!

Answer 23

Can you try this one?

Answer 24

Ok!

Answer 25

I have so many questions because i have an upcoming quiz on tuesday so i need to review sorry :)

Answer 26

the apothem a, of your pentgon is: a=8.26cm, so the area of your pentagon is: (perimeter*apothema)/2=\[A=\frac{ 12*5*8.26 }{ 2 }=247.8 cm ^{2} \]
the lateralarea S is:perimeter*altitude H, so:
\[S=12*5*48=2880cm ^{2}\]
then the total area S_tis: S+2*A, then:
\[S _{t}=S+2*A=2880+2*495.6=3375.6cm ^{2}\]
and the volume V, is A*, namely:
\[V=A*H=247.8*48=11,894.4cm ^{2}\]
Please, check all of my statements above!

Answer 27

What wll be the right section of then prism? Because as the formula states: LSA= Pe; where P is the perimeter of the right section and e is the length of the lateral edge. I am so confused with the right section term.

Answer 28

So, meaning to say, the height is equal to the lateral edge?

Answer 29

Am i correct?

Answer 30

I think the righ cross section is a pentagon like the bases. Area of a pentagon is equal, as I said befor, to the product between the perimeter of the pentagon and its apothema

Answer 31

I don't understand, what do you means by the "lateral edge", please?

Answer 32

Sorry, ...what do you mean...

Answer 33

The side of the prism

Answer 34

Lateral, only the side of the prism without the two bases

Answer 35

then Ok! the height is the lateral edge

Answer 36

Oh, so the height and the side of the prism are equal?

Answer 37

Not precisely, the height is equal to 48 cm, whereas the side is what I called the edge of each of the bases of your prism and it's equal to 12 cm

Answer 38

The sides of the base are not the same as the edges of the lateral surface, i guess?