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Calculate the volume #4 Answer Key

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1.05m 55cm It’s a Box! V= L x W x T = 1.05m x 55cm x 55cm Whoops, won’t work – the units don’t match. A little King Henry and change it to = 105cm x 55cm x 55cm Ballpark 100 x 50 x 50 = 250 000 = 317 625 cm 3

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28.8 cm 35.2cm 18cm It’s a Box! V= L x W x T = 35.2cm x 28.8cm x 18cm Ballpark 30 x 30 x 20 = 18 000 = 18 247.68 cm 3

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52mm 4.2cm 20.2cm It’s a Box! V= L x W x T = 20.2cm x 52mm x 4.2cm Whoops, won’t work – the units don’t match. A little King Henry and change it to = 20.2cm x 5.2cm x 4.2cm Ballpark 20 x 5 x 4 = 400 = 441.17 cm 3

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30cm 38 cm 5cm It’s a Triangle (a box cut diagonally in half Soooo… V= L x W x T /2 = 38cm x 30cm x 5cm Ballpark 40 x30 x 5 = 6000 = 5 700 cm 3

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8dm diameter It’s a Sphere! V= 4/3 π r 3 = 4/3 x 3.14 4dm x 4dm x 4dm (r3 = r x r x r) Ballpark 4/3 x 3 x 4 x 4 x 4 = 256 = 267.94 dm 3 (look at that unit!) Remember that the radius is half the diameter.

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20cm 75mm It’s a Cylinder V= π r 2 h = 3.14 x 75mm x 75mm x 20cm Whoops, won’t work – the units don’t match. A little King Henry and change it to = 3.14 x 75mm x 75mm x 200mm OR = 3.14 x 7.5cm x 7.5cm x 20cm It doesn’t matter which way, one will give an answer in mm 3 and one will give cm 3 Ballpark 3 x 7 x 7 x 20 = 2940 = 3532.5 cm 3

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15 m 55 m It’s a Cylinder V= π r 2 h = 3.14 x 27.5m x 27.5m x 15m Ballpark = 3 x 30 x 30 x 10 = 27 000 = 35 619.375 m 3

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19.5cm 6.5 cm It’s a Cylinder V= π r 2 h = 3.14 x 3.25cm x 3.25cm x 19.5cm Ballpark = 3 x 3 x 3 x 20 = 540 = 646.74cm 3

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980 mm 9cm It’s a Cylinder V= π r 2 h = 3.14 x 4.5cm x 4.5cm x 980mm Whoops, won’t work – the units don’t match. A little King Henry and change it to = 3.14 x 4.5cm x 4.5cm x 98.0cm Ballpark 3 x 5 x 5 x 100 =7500 = 6231.22 cm 3

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Dia = 2.5mm It’s a Sphere! V= 4/3 π r 3 = 4/3 x 3.14 1.25mm x 1.25mm x 1.25mm (r3 = r x r x r) Ballpark 4/3 x 3 x 1 x 1 x 1 = 4 = 8.18 mm 3 (look at that unit!)

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25.2 cm dia 35.5cm 19.5cm It’s a Sphere on top of a cone! V= 4/3 π r 3 for the sphere and V=1/3 π r 2 h for the cone There’s one more page! Sphere V= 4/3 π r3 = 4/3 x 3.14 x 12.6cm x 12.6cm x 12.6cm Ballpark 4/3 x 3 x 10 x 10 x 10 = 4000 = 8374.9 cm 3 Cone V=1/3 π r 2 h = 1/3 x 3.14 x 9.75cm x 9.75cm x 35.5cm Ballpark 1/3 x 3 x 10 x 10 x 30 = 3000 = 3532.2 cm 3 Now add together the Sphere and the cone! 8374.9 cm3 + 3532.2 cm3 = 11 907.1cm3

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Consider this a secret extra page – don’t tell anyone about it!!!! If you print out JUST THIS PAGE and solve the problem, I will give you extra credit for your effort! I found this cool box and I want to fill it with M&M’s to send to my brother. What would be the total volume of this box? You might find it helpful to sketch the box on the back of the paper to make it easier to break it into parts - try drawing it as if you were looking at the end of the box. 30cm 20cm 15cm 25cm Name: ____________________ Science Pd _______ EXTRA EXTRA CREDIT If an M&M takes up about. 8cm 3 of space, roughly how many would fit in the box?

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