Volume Question Help please

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Boe Nancy

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A traffic cone 60 cm height with a circular base of 15 cm and a circular top of radius 5 cm

a) Assuming the cone is solid find the volume of the cone

b)By considering the general format for a straight line y = a1 + b1 where a1 and b1 are constants

1) Find the value of a1 and b1 such that the line passes true the point ( 0,15) and (60,5)

2) Hence by rotating the resulting line 360 degrees about the x axis, verify your result to your answer in part (a)

c)A traffic cone is made up by pouring liquid plastic into a mould so that after solidifying, the resulting cone is hollow, consisting of a plastic shell of a certain thickness. Assuming that the dimension given in part (a) above are the outer dimension of the cone and the shell is 1cm thick, find the volume of the liquid plastic required for one con, by using the formula in part (a) (State any assumptions made or approximation)

d)The city council has proposed that a traffic cone with curved sides , would be more aesthetically pleasing as well as more economical since the volume will be less

Consider a curve y = a2/(b2 + c2) where a2 b2 and c2 are constants.



I COULD FIND THE VOLUME BUT DONT KNOW HOW TO DO THE REST OF IT I CANT DO

This is what i did so far

V= 1/3(3.14)(15)^2(60) = 14115.87cm^3
 
Last edited:
Boe Nancy said:
A traffic cone 60 cm height with a circular base of 15 cm and a circular top of radius 5 cm

a) Assuming the cone is solid find the volume of the cone

b)By considering the general format for a straight line y = a1 + b1 where a1 and b1 are constants

1) Find the value of a1 and b1 such that the line passes true the point ( 0,15) and (60,5)

2) Hence by rotating the resulting line 360 degrees about the x axis, verify your result to your answer in part (a)

c)A traffic cone is made up by pouring liquid plastic into a mould so that after solidifying, the resulting cone is hollow, consisting of a plastic shell of a certain thickness. Assuming that the dimension given in part (a) above are the outer dimension of the cone and the shell is 1cm thick, find the volume of the liquid plastic required for one con, by using the formula in part (a) (State any assumptions made or approximation)

d)The city council has proposed that a traffic cone with curved sides , would be more aesthetically pleasing as well as more economical since the volume will be less

Consider a curve y = a2/(b2 + c2) where a2 b2 and c2 are constants.
Click to expand...

What are your thoughts?

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This is what i did

I COULD FIND THE VOLUME BUT DONT KNOW HOW TO DO THE REST OF IT I CANT DO

This is what i did so far

V= 1/3(3.14)(15)^2(60) = 14115.87cm^3
I also found the equation of the line and then found the two constants a1 and b1

for the rest i am unsure
 
Boe Nancy said:
A traffic cone 60 cm height with a circular base of 15 cm and a circular top of radius 5 cm

a) Assuming the cone is solid find the volume of the cone

b)By considering the general format for a straight line y = a1 + b1 where a1 and b1 are constants

1) Find the value of a1 and b1 such that the line passes true the point ( 0,15) and (60,5)

2) Hence by rotating the resulting line 360 degrees about the x axis, verify your result to your answer in part (a)

c)A traffic cone is made up by pouring liquid plastic into a mould so that after solidifying, the resulting cone is hollow, consisting of a plastic shell of a certain thickness. Assuming that the dimension given in part (a) above are the outer dimension of the cone and the shell is 1cm thick, find the volume of the liquid plastic required for one con, by using the formula in part (a) (State any assumptions made or approximation)

d)The city council has proposed that a traffic cone with curved sides , would be more aesthetically pleasing as well as more economical since the volume will be less

Consider a curve y = a2/(b2 + c2) where a2 b2 and c2 are constants.



I COULD FIND THE VOLUME BUT DONT KNOW HOW TO DO THE REST OF IT I CANT DO

This is what i did so far

V= 1/3(3.14)(15)^2(60) = 14115.87cm^3
Click to expand...

That is not correct. The volume you found is a cone with pointed tip.

This traffic cone is a truncated cone - the tip is a circle (radius 5cm).

First draw a sketch of the truncated cone - represented by a pointed triangle with the tip cut-off.

Now figure out the total height of the (pointed) cone by considering similar triangles.

If a height of "h" was cut-off then:

(60+h)/15 = h/5

Calculate 'h' - then calculate total volume of the "truncated cone".
 
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