Volume and Surface Area
For any [b]rectangular prism[/b] you can find Volume with the following formula:[br][br][size=150][math]V=lwh[/math][br][br][/size]V= volume[br]l = length[br]w = width[br]h = height
[left]For [b]all prisms[/b] the volume is [br][br][math]V=Bh[/math][br][br]V = volume[br]B = Area of the base[br]h = height[/left]
[color=#ff0000]BE CAREFUL: The base is not always on the "bottom" of the figure[/color]
To find the volume of a [b]cylinder[/b] use this formula:[br][br][math]V=\pi r^2h[/math][br][br]V = volume[br]r = radius[br]h = height
[size=200]Now attempt questions 1-4 in the flipbook![/size]
What is the correct volume of the figure in #1?
[size=100]For all [b]pyramids[/b] the formula for volume is[br][br][math]V=\frac{1}{3}Bh[/math][br][br][/size]B = area of the base[br]h = height[br]
For all [b]cones[/b] the formula for volume is[br][br][math]V=\frac{1}{3}\pi r^2h[/math][br][br]r = radius[br]h = height[br]
[math]B=16^2=256[/math][br][math]h^2+8^2=17^2[/math](17 is the slant height)[br][math]h^2+64=289[/math][br][math]\sqrt{h^2}=\sqrt{225}=15[/math][br][br]plug into the formula above[br]h = 15[br]B = 256[br][br][math]V=\frac{1}{3}\left(256\right)\left(15\right)=1280[/math]cubic yards
[size=200]Now attempt questions 5-8 in the flipbook![/size]
What is the volume of the cone in #8?
[size=100]For all [b]rectangular prisms[/b] the formula for surface area is[br][br][math]SA=2lw+2lh+2wh[/math][br][br][/size]l = length[br]w = width[br]h = height[br]
[size=100]For all [b]prisms[/b] the formula for surface area is[br][br][math]SA=hp+2B[/math][br][br][/size]h = height between the bases[br]p = perimeter of the base[br]B = area of the base[br]
[size=100]For all [b]cylinders[/b] the formula for surface area is[br][br][math]SA=2\pi r^2+2\pi rh[/math][br][br][/size]r = radius[br]h = height[br]
[size=200]Now attempt questions 9-12 in the flipbook![/size]
What is the surface area of the figure in #11?
352.5 squared centimeters
[size=100]For all [b]pyramids[/b] the formula for surface area is[br][br][math]SA=\frac{1}{2}lp+B[/math][br][br][/size]l = slant height[br]p = perimeter of the base[br]B = area of the base[br]
[size=100]For all [b]cones[/b] the formula for surface area is[br][br][math]SA=\pi r^2+\pi rl[/math][br][br][/size]r = radius[br]l = slant height[br]
[size=200]Now attempt questions 13-18 in the flipbook![/size]
[color=#ff0000]Questions #14 and #16 you will need pythagorean theorem again to find the slant height. [/color]
What is the volume of the cone in #17?
[size=100]For all [b]spheres[/b] the formula for [b]volume[/b] is[br][br][math]V=\frac{4}{3}\pi r^3[/math][br][br][/size][br][br]For all [b]spheres[/b] the formula for [b]surface area is[br][br][/b][math]SA=4\pi r^2[/math][br][br]
[size=100]For all [b]spheres[/b] the formula for [b]volume[/b] is[br][br][math]V=\frac{4}{3}\pi r^3[/math][br][br][/size][br][br]For all [b]spheres[/b] the formula for [b]surface area is[br][br][/b][math]SA=4\pi r^2[/math][br][br]
[size=200]Now attempt questions 19-24 in the flipbook![/size]
What is the volume of the cone in #22?