6-6 Volume of prisms and Cylinders
Prism- a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. (The top and the bottom are the same. The sides are parallelograms.) Triangular Prism The bases are shaped like triangles V= 1/2bh (area of a triangle) x (height) Rectangular Prism The bases are shaped like rectangles V= lwh (area of the rectangle) x (height) If there are 5 or more sides to the base, the formula for volume is V=bh. The area of the base will be provided. All you have to do is multiply it by the height. Cylinder The bases are shaped like circles V= Πr2h (area of the circle) x (height)
Example: Find the volume of a rectangular prism with base 2 cm by 5cm and height 3 cm.
V= lwh V= (2)(5)(3) V= 30 Example: Find the volume. h=12in r=4in V=Πr2h V=3.14(16)(12) V=602.88 Example: A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds. First, you have to calculate the volume of the juice box. V= lwh V= 3(2)(4) V= 24in3 Next, triple one of the measurements. V=lwh V=9(2)(4) V=72in3 If you triple one of the measurements, the entire volume triples. The juice box will hold triple the amount of juice.
Example: A juice can has a radius of 2 in. and a height of 5 in
Example: A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. First, you have to find the volume of the juice can. V= Πr2h V= 3.14(4)(5) V= 62.8in3 Now, triple the height of the can and find the volume. V= 3.14(4)(15) V=188.4in3 188.4 ÷ 62.8 = 3 The volume increases by 3 times when you triple the height. Next, you have to triple the radius and find the volume. V=3.14(36)(5) V= 565.2 565.2 ÷ 62.8 = 9 When you triple the radius, the volume increases by 9 times.
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