3D Shapes and Circles

[highlight] [b]Prisms[/b][br] volume = area [multiply] length [length can be height if vertical] [/highlight] [highlight] [b]Arcs and Sectors[/b][br] sector area = ([theta] [divide] 360) [pi]r[squared] [r = radius][br] (arcs) [theta] [divide] 360 [multiply] [pi]d [d = diameter] [/highlight] [highlight] [b]Cylinders[/b][br] volume = [pi]r[squared] [multiply] h [h = height; r = radius][br] surface area = 2[pi]r[squared] + (2[pi]r [multiply] h) [r = radius; h = height] [/highlight] [highlight] [b]Spheres and Hemispheres[/b][br] sphere volume ---> (4 [divide] 3) [multiply] [pi]r[cubed][br] sphere surface area ---> 4 [multiply] [pi]r[squared] [br][br] hemisphere volume ---> (2 [divide] 3) [multiply] [pi]r[cubed][br] hemisphere surface area ---> (2 [multiply] [pi]r[squared]) + [pi]r[squared] [/highlight] [highlight] [b]Square Based Pyramids[/b][br] volume = (base area [multiply] height) [divide] 3[br] surface area = 2bs + b[squared] [b = base length; s = slanted height] [/highlight] [highlight] [b]Cones[/b][br] volume = (base area [multiply] height) [divide] 3 [its a circle based pyramid][br] surface area = ([pi] [multiply] radius [multiply] slanted height) + [pi]r[squared] [/highlight] [highlight] [b]Frustums[/b][br] -Frustums consist of 1 large cone, minus a smaller one[br] -The smaller cone's radius is proportional to the large cone's radius[br] -Therefore the smaller cone's height also follows the same ratio and vice versa[br] [br] -To find the volume of the [b]frustum[/b], calculate the volume of the large cone and find its difference with the small cone[br] [/highlight] [highlight] [b]Cuboids[/b][br] [i]a = height, b = width, c = depth(z axis)[/i][br] volume = a[multiply] b[multiply] c[br] surface area = 2(ab + ac + bc) [/highlight]