year 10 signpost h.w - need help with 2 questions about volume. (1 Viewer)

[Riot09]

"new"-year 10 signpost,need help with a few questions about volume.exercise 6:07

self-explanatory these are a few questions from my year 10 signpost textbook. There quite hard to fiqure out so please include working out.

i got just a few more questions left,that i haven't completed yet because i can't figure it out.So if you can please help.

Thanks in advance.

6:07

3.c

If any one has this text book this question is hard because they only give the vertical height and not the radius.So does anyone know what the radius is?.

4.Also this one is bit Weird too.

Calculate the volume of a “spherical shell" that has an inner radius of 5cm and an outer radius of 6cm.(give the anser in terms of pi).So what does this shell look like they didn't inlcude a diagram.

5.b what is the smallest radius a sphere can have if it has to have a greater volume than 5000cm^3.

and finally 5.c A sphere has to have a volume of 1m^3.What is the radius of the sphere?

 

[annarh-saur]

Hey, it's the 5.3 signpost yeh? I'm just gonna type up my working out from my maths book..

Ex 6:05
Q4.
d) 4000 = 1/3 x 2x^2 x 60
4000 = 20 x 2x^2
4000 = 40x^2
(squareroot)100 = (sqaureroot)x^2
= 10 cm

the long is "twice" the wide
therefore, dimensions = 10cm and 20 cm

Ex 6:06
Q5.
d) V= 1/3 x pi x 10^2 x 10
= 1047.197
1047.197 = pi x 5^2 x h
1047.197 = 25pi x h
1047.197/25pi = h

therefore, height = 13 1/3 cm

hope that helps

 

[ninetypercent]

4.d

A rectangle that is twice as long than it is wide forms the base of a rectangular pyramid that is 60cm high.If the volume of the pyramid is 4000cm^3,what are the dimensions of the rectangle.

Let the length width be w
the length is therefore 2w

Volume = 1/3 x 2w x w x 60 = 40w^2
4000 = 40w^2
100 = w^2
w = 10 (as w>0)
but the length is twice its width

therefore, length is 10 x 2 = 20 cm

length = 20 cm
width = 10cm

 

[4025808]

self-explanatory these are 2 questions from my year 10 signpost textbook. There quite hard to fiqure out so please include working out.As the answers are at the back of the book but there is no working out.

6:05

4.d

A rectangle that is twice as long than it is wide forms the base of a rectangular pyramid that is 60cm high.If the volume of the pyramid is 4000cm^3,what are the dimensions of the rectangle.

(Is there a short/algebraic way to work out this question other than using trial and error. The answer is lenght =20cm and width =10cm

6:06

5.d

A conical flask has a radius of 10cm and a height of 10cm.The contents of the cone are emptied into a cylinder with a radius of 5cm.How high must the cylinder be to hold the contents of the cone?

The answer is 13 and one third or 13.3333

Thanks in advance.

6.05; 4 d) It states that the rectangle is twice as long than it is wide. Make the length '2x' and make the width 'x' because the length is two times the width.

the length times the width would equal the area, so therefore, 2x times x would equal to 2x^2

Because the area is 200cm^2, therefore it would equal to 2x^2. Then you would have to divide 200 by 2x^2.

Then 200/2 = 100 = x^2
x = (+/-)10

Because a length can only be positive, therefore it is 10cm.

Then if the width was x, then the width is 10cm, and then the length would equal 20cm because it is double.

 

[Amogh]

aw man
you guys beat me to it
=.=

lol riot
RELAX for a week or so
atleast
SCs barely over =)

 

[Amogh]

Re: "new"-year 10 signpost,need help with a few questions about volume.exercise 6:07

6:07

3.c

If any one has this text book this question is hard because they only give the vertical height and not the radius.So does anyone know what the radius is?.

The height of that hemisphere is its radius as well.
The height of the cylinder and cone is same as that of the hemisphere.

4.Also this one is bit Weird too.

Calculate the volume of a “spherical shell" that has an inner radius of 5cm and an outer radius of 6cm.(give the anser in terms of pi).So what does this shell look like they didn't inlcude a diagram.

Look at the picture at the bottom
They've simply subtracted the volume of the small tank from that of the larger one.

5.b what is the smallest radius a sphere can have if it has to have a greater volume than 5000cm^3.

4/3*pi*r^3=5000
pi*r^3=(5000*3)/4
r^3=3750/pi
r = cuberoot(3750/pi) = 10.6...=11 cm

and finally 5.c A sphere has to have a volume of 1m^3.What is the radius of the sphere?

do the same as 5 b
equation is 4/3*pi*r^3 = 1
now solve for r
note: it says round of to the nearest cm., although the answer in the book is in metres
lol



soz for the late reply

 

[Riot09]

Re: "new"-year 10 signpost,need help with a few questions about volume.exercise 6:07

thats alright,thanks.