VOLUME By: Mateo Alzate and Khoi Ngo Volume: Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. Its units are always "cubic", that is, the number of little element cubes that fit inside the figure. For Example l A= l x w

A= 8cm x 2cm

A= 16 cm 2 V= lwh 3 cm 3cm 3cm V= s

V= 3cm x 3cm x 3cm

V= 27 cm 3 3 10 cm 6cm 4cm V= lwh

V= 10cm x 4cm x 6cm

V= 240cm 3 V= Volume

l = length

w= width

h= height V= lwh

V= 2cm x 2cm x 8cm

V= 32 cm 3 Rectangular Pyramid 4cm 4cm 7cm V= 1/3 lwh

V= 1/3 (7cm x 4cm x 4cm)

V= 37.3 cm 3 Cylinder. 10m 6m V=πr h

V= 3.14 x 3cm x 10cm

V= 282.6cm 2 2 3 Cone V= 1/3 πr h 2 4km 7.5km 4km 8.5km ? Pythagorean Theorem A + B = C 2 2 2 C - A = B

8.5km - 4km = B

72.25 - 16 = 56.25

√ 56.25= 7.5

7.5= B 2 2 2 2 2 2 V= 1/3 πr h

V= 1/3 ( π x 4km x 7.5km)

V= 125.7 km 2 2 3 SPHERE V= 4/3 πr 3 12m V= 4/3 πr

V= 4/3 π x 12

V= 7238.2km 3 3 3 V= 7238.2km / 2

V= 3619.1km 2 2 Relations Between Shapes. A right pyramid is related to a right prism. A right cone and a cylinder. A sphere and a Cylinder 8cm 2cm 8cm 2cm 2cm Volume of Composite Objects. To find the volume of this composite object, you will have to find the volume of the hemispheres first. V= 4/3 πr

V= 4/3 (3.14 x 1)

V= 4.186' 2 3 V= πr h

V= 3.14 x 1 x 6

V= 18.84' 3 2 V= 23.026' 3 Then find the volume of the Cylinder Then add them together. First find the volume of the rectangular prism 3cm V= lwh

V= 5cm x 5cm x 7cm

V= 175 cm 3 Then find the volume of the cone. V= 1/3πr h

V= 1/3 (3.14 x 2.25cm x 5cm

V= 11.775cm 2 3 5cm Now subtract the volume of the cone from the volume of the rectangular prism. V= 175cm - 11.775 cm

V= 163.225 cm 3 3 3 A Mathematician says: Pi r squared

A Baker replies: Pi r round not squared, cake is squared. A Mathematician says: Pi r squared.

The baker replies: Pie are round! not square! Cake is square!

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# Volume and Surface Area

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