How to find h in terms of x?

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Can someone please explain to me how to do question 31 a? Thank!

5 Answers
Apr 23, 2018

h=10002πxx

Explanation:

for 31a, you need the formula for the total surface area of a cylinder.

the total surface area of a cylinder is the same as the total of both circular surfaces (top and bottom) and the curved surface area.

the curved surface area can be considered as a rectangle (if it were to be rolled out). the length of this rectangle would be the cylinder's height, and its width would be the circumference of a circle on the top or bottom.

the circumference of a circle is 2πr.
height is h.

curved surface area = 2πrh.

the area of a circle is πr2.

area of top and bottom circles: 2πr2

the total surface area of the cylinder is 2πrh+2πr2, or 2πr(h+r).

we are given that the total surface area of the cylinder is 1000cm2.

this means that 2πr(h+r)=1000.

then, h+r=10002πr

h=10002πrr

in this question, the radius is actually denoted as x, so h in terms of x would be

h=10002πxx

Apr 23, 2018

h=500πx+x

Explanation:

The radius of the base is x. The circumference of the base must be 2πx.

So the surface area of the curved face is 2πxh. From the description it sounds like we're to include the surface are of the end caps as well, there are two, each area πx2.

So the total surface area is

1000=2πxh+2πx2

πxh=500πx2

h=500πxx

Apr 23, 2018

The surface area of a cylinder is:

A=2πxh+2πx2

We are given that A=1000 cm2

1000 cm2=2πxh+2πx2

Flip the equation:

2πxh+2πx2=1000 cm2

Multiply both sides by 12πx:

h+x=1000 cm22πx

Subtract x from both sides of the equation:

h=1000 cm22πxx this is h in terms of x

Apr 23, 2018

h=500πxx

Explanation:

The surface area is made up of the two circles and the rectangular body
The circles area is πx2 so double this 2πx2
The height of the rectangle is h and the width of the rectangle is the circumference of the cylinder.
Circumference=πD=2xπ
The area of the rectangle =2xπ×h
We are given the surface area is 1000cm2
So 2πx2+2πxh=1000

2πx(x+h)=1000

x+h=10002πx

x+h=500πx

h=500πxx

Apr 23, 2018

h= 10002πx22πx, i.e, h=10002πxx.

Explanation:

The total surface area of the cylinder will be the area of its two circular ends plus the area of the outside of the cylinder.

Area of one end=πr2. Area of outside of cylinder=2πrh

So the total area of the cylinder is 2πr2 +2πrh. we are given that the radius r=x, so ,

Total area of the cylinder is 2πx2+2πxh=1000 and making h the subject of this equation gives the above answer. Hope this was helpful.