What are the steps for using a compass and straightedge to construct a square? drag the steps and drop them in order from start to finish. construct a circle with point h as the center and a circle with point j as a center with each circle having radius hj .construct horizontal hj¯¯¯¯¯ construct a circle with point m as the center with radius mj .label the point of intersection of the two circles above hj¯¯¯¯¯ , point k, and the point of intersection of the two circles below hj¯¯¯¯¯ , point l. construct kl¯¯¯¯¯ , the perpendicular bisector of hj¯¯¯¯¯ , intersecting hj¯¯¯¯¯ at point m. construct hn¯¯¯¯¯¯ , nj¯¯¯¯¯ , jo¯¯¯¯¯ , and oh¯¯¯¯¯¯ to complete square hnjo .label the point of intersection of circle m and kl¯¯¯¯¯ closest to point k, point n, and the point of intersection of circle m and kl¯¯¯¯¯ closest to point l, point o.

The steps for using a compass and straightedge to construct a square are as follows:

1. Construct horizontal HJ¯¯¯¯¯ .

2. Construct a circle with point H as the center and a circle with point J as a center with each circle having radius HJ .

3. Label the point of intersection of the two circles above HJ¯¯¯¯¯ , point K, and the point of intersection of the two circles below HJ¯¯¯¯¯ , point L.

4. Construct KL¯¯¯¯¯ , the perpendicular bisector of HJ¯¯¯¯¯ , intersecting HJ¯¯¯¯¯ at point M.

5. Construct a circle with point M as the center with radius MJ .

6. Label the point of intersection of circle M and KL¯¯¯¯¯ closest to point K, point N, and the point of intersection of circle M and KL¯¯¯¯¯ closest to point L, point O.

7. Construct HN¯¯¯¯¯¯ , NJ¯¯¯¯¯ , JO¯¯¯¯¯ , and OH¯¯¯¯¯¯ to complete square HNJO .

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.