SURFACE AREA and VOLUME with BASE 10 BLOCKS

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Presentation transcript:

SURFACE AREA and VOLUME with BASE 10 BLOCKS INTRODUCTION PROBLEM 1 PROBLEM 5 PROBLEM 2 PROBLEM 6 PROBLEM 3 PROBLEM 7 PROBLEM 4 PROBLEM 8 PROBLEM 9

10 cm 3 100 cm 3 1 cm 3 1000 cm 3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

BASE 10 BLOCKS VALUES FOR VOLUMES USING PRISM VOLUME FORMULA: Volume for each individual Base 10 Block 10 1 1 1 10 10 1 1 10 1 10 10 Volume: Volume: Volume: Volume: V = Bh V = Bh V = Bh V = Bh V = (10x10)x10 V = (10x10)x1 V = (1x10)x1 V = (1x1)x1 V = 100x10 V = 100x1 V = 10x1 V = 1x1 V = 1000 cubic units V = 100 cubic units V = 10 cubic units V = 1 cubic units PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

BASE 10 BLOCKS VALUES FOR VOLUMES: 1 cm 3 10 cm 3 100 cm 3 1000 cm 3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

BASE 10 BLOCKS VALUES FOR AREAS: Each PRISM has 6 faces 2(10x10) 2(1X1) 4(10X1) 10x10 6(1X1) 4(10X1) 6 cm 2 6(10x10) 2(1x1)+4(10x1) 6(100) 2(1)+4(10) 2(10x10)+4(10x1) 600 cm 2 2(100)+4(10) 2+40 42 cm 2 200+40 240 cm 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

BASE 10 BLOCKS VALUES FOR AREAS: 6 cm 2 42 cm 2 240 cm 2 600 cm 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

FIND THE VOLUME FOR THE FIGURE BELOW: Volume for each individual Base 10 Block 10 1000 cu 10 10 Volume: 1000 cu 1000 cu V = Bh V = (10x10)x10 Total Volume = 3(1000 cu) V = 100x10 = 3000 cu V = 1000 cubic units PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

FIND THE SURFACE AREA FOR THE FIGURE BELOW: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y z x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y Right and Left Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y Top and Bottom Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y Front and Back Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y ALL Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y ALL Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(300) y 100 x 100 z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(200) y 100 100 x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(200) y 100 x 100 z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(300) + 2(200) + 2(200) = 600 + 400 + 400 y 100 100 100 100 x 100 100 z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

TOP VIEW FRONT VIEW RIGHT VIEW Eliminating redundant views draw an orthographic drawing of the previous figure: TOP VIEW FRONT VIEW RIGHT VIEW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Now draw an isometric drawing of the figure (corner view): PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Draw a FOUNDATION drawing of the ISOMETRIC figure: Using the top view: FOUNDATION DRAWING 2 1 Indicates 2 levels Indicates 1 level PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

FIND THE VOLUME FOR THE FIGURE BELOW: Volume for each individual Base 10 Block 10 10 10 Volume: V = Bh V = (10x10)x10 Total Volume = V = 100x10 V = 1000 cubic units PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

FIND THE VOLUME FOR THE FIGURE BELOW: Volume for each individual Base 10 Block 1000 cu 10 1000 cu 10 1000 cu 10 Volume: 1000 cu V = Bh V = (10x10)x10 Total Volume = Total Volume = 4(1000 cu) V = 100x10 = 4000 cu V = 1000 cubic units PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

FIND THE VOLUME FOR THE FIGURE BELOW: Volume for each individual Base 10 Block 10 10 10 Volume: V = Bh V = (10x10)x10 Total Volume = 4(1000 cu) V = 100x10 = 4000 cu V = 1000 cubic units PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

FIND THE SURFACE AREA FOR THE FIGURE BELOW: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y z x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y Right and Left Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y Top and Bottom Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y Front and Back Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

y ALL Views x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

ALL Views y x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(300) y 100 x 100 z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(300) y 100 100 x z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(300) y 100 x 100 z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Total Surface Area = 2(300) + 2(300) + 2(300) = 600 + 600 + 600 y 100 100 100 100 x 100 100 z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

TOP VIEW FRONT VIEW RIGHT VIEW Eliminating redundant views draw an orthographic drawing of the previous figure: TOP VIEW FRONT VIEW RIGHT VIEW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Now draw an isometric drawing of the figure: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Draw a FOUNDATION drawing of the ISOMETRIC figure: Using the top view: FOUNDATION DRAWING 2 1 Indicates 2 levels Indicates 1 level 1 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Find the volume for the shape below: 10 c.u 100 c.u. 1000 c.u. 4x 1000 4000 600 20 6x 100 2x 10 4620 VOLUME = 4620 c.u. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Find the total surface area for the shape below: 2 sq. u. x 2 Front and Back Find the total surface area for the shape below: 2 sq. u. FRONT VIEW 30 sq. u. 200 262 100 sq. u. 60 2 524 100 sq. u. 30 sq. u. Surface Area =524 + 880 + 800 = 2204 square units x 2 Right and Left 100 sq. u. 100 sq. u. 40 sq. u. TOP VIEW 400 440 RIGHT VIEW 40 100 sq. u. 880 100 sq. u. x 2 Top and Bottom 400 100 sq. u. 100 sq. u. 100 sq. u. 100 sq. u. 800 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Find the total surface area for the shape below: x 2 Front and Back Find the total surface area for the shape below: FRONT VIEW 200 262 60 2 524 Surface Area =524 + 880 + 800 = 2204 square units x 2 Right and Left TOP VIEW 400 440 RIGHT VIEW 40 880 x 2 Top and Bottom 400 800 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Build the figure represented in the orthographic views below: FRONT VIEW TOP VIEW RIGHT VIEW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Draw an isometric drawing of the figure: FRONT RIGHT PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

TOP VIEW RIGHT VIEW FRONT VIEW Draw an orthographic drawing of the figure: TOP VIEW RIGHT VIEW FRONT VIEW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Surface Area =1000 + 800 + 600 = 2400 square units Find the surface area: x 2 Top and Bottom TOP VIEW 100 sq. u. 100 sq. u. 300 600 100 sq. u. x 2 Right and Left RIGHT VIEW 100 sq. u. 100 sq. u. FRONT VIEW 400 800 x 2 Front and Back 100 sq. u. 100 sq. u. 100 sq. u. 500 100 sq. u. 100 sq. u. 100 sq. u. 100 sq. u. 1000 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Surface Area =1000 + 800 + 600 = 2400 square units Find the surface area: x 2 Top and Bottom TOP VIEW 300 600 x 2 Right and Left RIGHT VIEW FRONT VIEW 400 800 x 2 Front and Back 500 1000 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved