Volume of SolidsVolume of Solids (2)(2)

Today’s lesson will cover…Today’s lesson will cover…

finding volume of cylinders and conesfinding volume of cylinders and cones

using formulas to solve problems using formulas to solve problems involving volume of prisms and cubes.involving volume of prisms and cubes.

What we must first knowWhat we must first know

How to calculate the How to calculate the area of a circle.area of a circle.

2*rAreacircle Definition of Volume

the amount of 3-dimensional space occupied by an object

Proportions and ratios

CylindersCylinders

The bases of cylinders The bases of cylinders are circles. To find the are circles. To find the area of the base use pi*rarea of the base use pi*r22

After you find the base After you find the base area (B), multiply by the area (B), multiply by the height to get the volumeheight to get the volume

Volume of Cylinder = BhVolume of Cylinder = Bh

Base area

height

CylindersCylinders Find the volume of the soda can Find the volume of the soda can

shown belowshown below

5 inches

2 ¾ inches

Calculate the area of the base

A = 3.14*(2.75)2

A = 3.14*7.5625

A =23.746 square inches

Multiply base area times height

23.746 in2 * 5 in

118.73 in3

Mr. Emory bought a 5 gallon bucket of roof sealant for the Mr. Emory bought a 5 gallon bucket of roof sealant for the house his construction class was building. The dimensions of house his construction class was building. The dimensions of the bucket are shown below. Using 1 gallon = 231 cubic the bucket are shown below. Using 1 gallon = 231 cubic inches, determine the depth of sealant in the bucket if there inches, determine the depth of sealant in the bucket if there were 808 cubic inches left over.were 808 cubic inches left over.

Given informationGiven information 1 gallon = 231 cubic inches1 gallon = 231 cubic inches 5 gallon bucket5 gallon bucket 808 cubic inches left over808 cubic inches left over Diameter = 11.5 inchesDiameter = 11.5 inches Height of cylinder = 14.5 inchesHeight of cylinder = 14.5 inches

QuestionQuestion What is the depth (height) of the What is the depth (height) of the

fluid remaining in the bucket.fluid remaining in the bucket. 11.5 in

14.5 in

Mr. Emory bought a 5 gallon bucket of roof sealant for the Mr. Emory bought a 5 gallon bucket of roof sealant for the house his construction class was building. The dimensions of house his construction class was building. The dimensions of

the bucket are shown below. Using 1 gallon = 231 cubic the bucket are shown below. Using 1 gallon = 231 cubic inches, determine the depth of sealant in the bucket if there inches, determine the depth of sealant in the bucket if there

were 808 cubic inches left over.were 808 cubic inches left over.11stst determine the volume remainingdetermine the volume remaining

Full bucket – left over = amount usedFull bucket – left over = amount used

1155in1155in33-808 in-808 in33 Volume remaining = 347 in Volume remaining = 347 in33

22ndnd find the area of the base find the area of the base

Area of circle = Area of circle = ππrr22 = (3.14)(11.5/2) = (3.14)(11.5/2)22 = 103.82 in = 103.82 in22

33

11555

231

1inx

x

gallons

in

gallon

Mr. Emory bought a 5 gallon bucket of roof sealant for the Mr. Emory bought a 5 gallon bucket of roof sealant for the house his construction class was building. The dimensions of house his construction class was building. The dimensions of

the bucket are shown below. Using 1 gallon = 231 cubic the bucket are shown below. Using 1 gallon = 231 cubic inches, determine the depth of sealant in the bucket if there inches, determine the depth of sealant in the bucket if there

were 808 cubic inches left over.were 808 cubic inches left over.

Now we can find the height by using Now we can find the height by using the Volume formula for a cylinderthe Volume formula for a cylinder

V = BhV = Bh

347 in347 in33 = 103.82 in = 103.82 in2 2 * h* h

h = 3.34 inchesh = 3.34 inches

ConesCones

The base of a cone is a The base of a cone is a circle. To find the area of circle. To find the area of the base use pi*rthe base use pi*r22

After you find the base After you find the base area (B), multiply by 1/3 area (B), multiply by 1/3 and by the height to get and by the height to get the volumethe volume

Volume of Cone = 1/3 BhVolume of Cone = 1/3 Bh

Base area

Find the area of a cone with a Find the area of a cone with a 6 inch radius and 5 inch height6 inch radius and 5 inch height

Volume = 1/3*B*hVolume = 1/3*B*h B = 3.14(6in)B = 3.14(6in)22 = 113.04 in = 113.04 in22

h = 5 inchesh = 5 inches

V = 1/3 * 113.04 inV = 1/3 * 113.04 in22*5in *5in V = 118.4 inV = 118.4 in33