5 Minute Check Find the volume. Complete on homework. 1.2. 3.4.

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Presentation transcript:

5 Minute Check Find the volume. Complete on homework

5 Minute Check Find the volume. Complete on homework. 1.

5 Minute Check

Find the volume. Complete on homework. 2.

5 Minute Check

Find the volume. Complete on homework. 3.

5 Minute Check Find the volume. Complete on homework. 3. B = 3 · 2 ÷ 2 = 3 V = Bh V = 3 · 4 = 12m³

5 Minute Check Find the volume. Complete on homework. 4.

5 Minute Check Find the volume. Complete on homework. 4. B = 6 · 2 ÷ 2 = 6 V = Bh V = 6 · 7 = 42cm³

Friday, March 13 Chapter Surface Areas of Rectangular Prisms

Objective: To find the surface area of rectangular prisms.

Surface Areas of Rectangular Prisms The surface area (SA) of a three dimensional figure is the outer face or exterior boundary of the figure.

Surface Areas of Rectangular Prisms There are two main formulas to find the surface area of a rectangular prism. Rectangular Prism Formula Universal Prism Formula

Surface Areas of Rectangular Prisms The advantage in using the Universal Prism Formula is that it can used with triangular prisms in the next lesson. Otherwise a new formula will need to be memorized.

Surface Areas of Rectangular Prisms Rectangular Prism Formula The surface area (SA) of a rectangular prism is 2 x length x width + 2 x height x width + 2 x length x height, or SA = 2lw + 2hw +2lh

Surface Areas of Rectangular Prisms Universal Prism Formula The formula to find the surface area (SA) of a prism is 2 x Area of the Base + height x perimeter of the Base, or SA = 2B + hp

Surface Areas of Rectangular Prisms In a three –dimensional shape the Base (B) is area of the bottom and top of the shape and determines the name of the prism.

Surface Areas of Rectangular Prisms SA = 2B + hp Area of the Base (B) = lw Perimeter of Base(p) = w + l + w + l height (h) = The distance from Base to Base.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp To Find the SA of a rectangular prism. Step 1 – Find the area of the base.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 5 · 7 = 35 To Find the SA of a rectangular prism. Step 1 – Find the area of the base. (The base will be on the face it is resting on)

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 35 To Find the SA of a rectangular prism. Step 2 – Find the perimeter of the base.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 35 p = =24 To Find the SA of a rectangular prism. Step 2 – Find the perimeter of the base.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 35 p =24 To Find the SA of a rectangular prism. Step 3 – Find the height.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 35 p =24 h = 4 To Find the SA of a rectangular prism. Step 3 – Find the height.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 35, p =24, h = 4 To Find the SA of a rectangular prism. Step 4 – Substitute the measurements in for the correct variables and solve.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism using SA = 2B + hp B = 35, p =24, h = 4 SA = 2 · · 24 SA = = 166 ft² To Find the SA of a rectangular prism. Step 4 – Substitute the measurements in for the correct variables and solve.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. w = 5, l = 7, h = 4 SA = 2lw + 2hw +2lh SA = 2·7·5 + 2·4·5 + 2·7·4 SA = = 166 ft²

Surface Areas of Rectangular Prisms Another way to find the SA is to deconstruct the shape into a net. The surface area (SA) of a prism is the sum of all the areas of it’s faces.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. With a net, compute the area if it was a composite figure.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. ?

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. 35 ?

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. 35 ?

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism ?

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism ?

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism ?

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = = 166 ft²

Surface Areas of Rectangular Prisms You may either be given the 3D drawing or a net and asked to determine the surface area. You can construct a net from a 3D drawing, if you wish.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. Do this on your own.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· B

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2·12 + h

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· · p

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· · 14

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· · 2 SA =

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. B = 12, p = 14, h = 2 SA = 2· · 2 SA = = 52m²

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. 4m 2m 3m SA = =52m² (Bottom)

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. Do this on your own.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2·B

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· p

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· ·h

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· ·6

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 2· ·6 SA =

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. B = 33.6, p = 23.6, h = 6 SA = 2· ·6 SA = SA = cm²

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. Do this on your own.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = = 168yd²

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. w = 9, l = 6, h = 2 B = 54, p = 30 SA = 2 · · 30 = 168yd² SA = 2·6·9 + 2·2·9 + 2·6·2 = 168yd²

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = =800 in²

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. w = 15, l = 10, h = 10 B = 150, p = 50 SA = 2 · · 50 = 800 in² SA = 2·10·15 + 2·10·15 + 2·10·10 = 800 in²

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism.

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. SA = 6 · 6.76 = km² 6.76

Surface Areas of Rectangular Prisms Find the SA of the rectangular prism. w = 2.6, l = 2.6, h = 2.6 B = 6.76, p = 10.4 SA = 2 · · 10.4 = km² SA = 2·2.6· ·2.6· ·2.6·2.6 = km²

Surface Areas of Rectangular Prisms What is the surface area of the video game box?

Surface Areas of Rectangular Prisms What is the surface area of the video game box? w = 16, l = 15, h = 11 B = 240, p = 62 SA = 2 · · 62 = 1162cm²

Surface Areas of Rectangular Prisms A geode is being sent as a gift. It is packed in a box that measures 7 inches long, 3 inches wide, and 16 inches tall. What is the surface area of the box? Do this on your own.

Surface Areas of Rectangular Prisms A geode is being sent as a gift. It is packed in a box that measures 7 inches long, 3 inches wide, and 16 inches tall. What is the surface area of the box? w = 3, l = 7, h = 16 B = 21, p = 20 SA = 2 · · 20 = 362in² SA = 2·7·3 + 2·16·3 + 2·7·16 = 362in²

PARCC 5

PARCC 6 6. Small cubes with edge lengths of ¼ inch will be packed into the right rectangular prism shown. How many small cubes are needed to completely fill the right rectangular prism?

PARCC 6 6. Small cubes with edge lengths of ¼ inch will be packed into the right rectangular prism shown. How many small cubes are needed to completely fill the right rectangular prism? 18 · 20 · 15 =

PARCC x 4.39 =

PARCC x 4.39 =

Surface Areas of Rectangular Prisms Agenda Notes Homework– Homework Practice Due at the end of the period Chapter 9.9/6.10 Test – Thursday, March 19