What is the length of a diagonal of a square with a side length of 8? A. 4
B. 42
C. 43
D. 82

D. 8

Step-by-step explanation:

To find the diagonal of the square, you can use the Pythagorean theorem* to find the hypotenuse since the diagonal cuts the square into two right triangles with legs of 8 units in length:

If in a^2 + b^2 = c^2, a = 8 and b = 8,

8^2 + 8^2 = c^2 (put 8 as both the leg lengths in the equation)

128 = c^2 (calculate 8^2 and then add the two terms together)

c = 8 (square both sides)

So, the length of the diagonal is 8 units

*the Pythagorean theorem is a theorem used to find the sides lengths of a right triangle: a^2 + b^2 = c^2. a and b are the legs of the triangle, and c is the hypotenuse.

are you an artist's daughter? cuz dang you a fine piece of art, girl.

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.