<ol>
<li><p>yfrog</a> Photo : Shared by</p></li>
<li><p>yfrog</a> Photo : Shared by</p></li>
</ol>
<p>Second question:</p>
<p>Subsitute 0 for x which gives the coordinates of P as (0,9).
Then solve the equation of the curve(by subst. 0 for y) which gives x=1.5 and 3.
Since point R is leftwards than the next point of intersection between the curve and the x-axis, the coordinates of point R must be (1.5,0)
So you now have the coordinates of points O,P and R. Then use distance formula or simply sight to find the length of OP and OR(9 & 1.5). Area of rect. OPQR then = OP x OR = 9x1.5=13.5.</p>
<ol>
<li>Note volume of cone is 1/3 of that of a cylinder. Note that the height of containers is same. There, we just need to find out the height till which the liquid will fill up in the cylinder. Since volume of liquid in both cases is equal, therefore,</li>
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<p>1/3<em>π</em>(r^2)<em>h = π</em>(r^2)*H … h=height of cone. H=height of liquid in cylinder.
h/3=H.</p>
<p>Since height of both cone and cylinder is same (6 units)
therefore, height of liquid in cylinder = 6/3 = 2 units.</p>
<ol>
<li>y= 2x² - 9x + 9. y-intercept = (0,9)
therefore, you correctly, found out the length of the rectangle to be 9 units.
factorize y to find a value for x.</li>
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<p>y = 2x² - 9x + 9 = 0
2x² - 6x -3x + 9 = 0
2x(x-3) - 3(x-3) = 0
(x-3)(2x-3) = 0</p>
<p>which gives us x = 3 or x = 1.5</p>
<p>It can be seen from the graph (the points where the graph cuts the x-axis) that point R has the co-ordinates (1.5 , 0)</p>
<p>Therefore, width = 1.5</p>
<p>Area of rectangle = 1.5*9 = 13.5 square units.</p>
<p>Hope I helped :)</p>
<p>First question:
First, find the volume of both the solids. For the cone volume=(1/3) x pi x 3^2 x 6 = 18 pi
For the cylinder, volume = pi x 3^2 x 6 = 54 pi
Then find the ratio of the volume of the cone to the volume of the cylinder which is 1:3. Since when the water from the cone is poured into the empty cylinder, the radius of the cylinder(formed by the water) is still the same as the radius it had when the water was in the cone, the ratios of volumes of the two solids must be equal to the ratios of theor height. </p>
<p>Remembering that the ratio of volumes was 1:3 and height of the cone was 6 inches, now the height of the water level must be one third of the heigjt of the cone that is 2 inches. So the height will be 2 inches. </p>
<p>Hope the answers helped! 
:)</p>
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<p>@aashish2025 If I subs. 0 for y, y= 2x^2 -9x +9</p>
<p>it will be like this 0=2x^2 -9x +9, That’s not enough for me to carry on. sorry but i am just really bad with geometric shapes.</p>
<p>Mathnub, I solved the equation for you in my explanation above :)</p>
<p>I’m not exactly sure where you are struggling. I’ll try to be clear.
There is a rectangle on this graph that we need to find its area, using the conventional area rule for a rectangle that is Base multiplied by the height. to do so, we need to find some points on the graph. Since we have a parabola that crosses the rectangle at two points (one a the top left and one at the bottom right) then we just need to find those only two points by the given equation for the parabola. Since P is at the origin then you go up by some factor. then you can easily know that for the point P the x value is 0, but what we need is not x: we need y. you can substitute 0 for x in the equation of the the parabola but there really is no need for that, since you already know that the parabola meets the y-axis at 9, which indicates that the whole height of the rectangle is 9. Now all what you got to do is find the value of R. since R is at 0 in the Y axis at the right by a few factors, you can substitute in the equation Y=0 and then you’ll have the form x^2-9x+9=0, you can factor that out or use the quadratic formula to find the value of the roots of the equation (where the parabola meets the x axis), The roots will be 1.5 and 3… we’re going to use the former since we know that it has definitely hit the smaller value not the bigger value. so now we know that the distance for the base will be 1.5, 9x1.5 = 13.5 square units.</p>