When baking a cake, you have a choice of the following pans: 1. a round cake pan that is 2 inches deep and has a 7-inch diameter
2. a 6 inch × 9-inch rectangular cake pan that is 2 inches deep

Which of these pans has the larger volume? Justify your answer.

round cake - 82.42 in^2

rectangular cake - 114 in^2

Round cake:

d = 7 in

r= d/2 = 7 in /2 = 3.5 in

h = 2

The surface area of a cylinder is: A = 2pie r^2 + 2pie rh The surface are of the round cake (cylindrical cake) excluding the bottom is

Area = 2pie r^2 + 2pie rh - pie r^2

Area = pie r^2 + 2pie rh

Area = 3.14 * 3.5² + 2 * 3.14 * 3.5 * 2

= 38.46 + 43.96

= 82.42 in^2

Rectangular cake:

w = 6 in |= 9 in h = 2 in

The surface area of a rectangle

A = 2wl + 2wh + 2lh

The surface are of the rectangular cake excluding the bottom is

A = 2wl + 2wh + 2lh - wl

A = wl + 2wh + 2lh

A = 6 * 9 + 2* 6 * 2 +2 *9 * 2

= 54 + 24 +36

= 114 in^2

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral