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Warm Up

Find the Surface area of each rectangular Prism to the nearest tenth

5.5cm

2.3cm10cm

1. 2. 7.8 in.

6.2 in.5.4 in.

181.3cm2 247.9 in2

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Warm Up

Find the surface area of Cylinders:

4. r = 6mm, h = 10 mm 603.2mm2

5. r = 3.5 ft, h = 24 ft 604.8ft2

3. Write the formula for the surface area of a Cube in which each edge measures x units.

Surface area = 6x 2

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Surface Area of a PrismThe surface area of a prism is the sum of the areas ofall the sides of the prism. The formula for the surfacearea of a prism therefore depends on the type of prism.

Surface Area of a CylinderThe surface area of a cylinder is the sum of the areasof the two bases and the lateral face of the cylinder.

surface area of a cylinder = 2*r2 + 2rh

Lets review what we have learned in the last lesson

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Types of prism

The name of a prism depends upon its base polygons.

If the bases are triangles, then it is a TRIANGULAR prism.

A RECTANGULAR prism has bases which are rectangles . The other types of prisms are pentagonal prism, hexagonal

prism and octagonal prism.

Surface Area of prism:

Surface Area of any prism = Lateral area + Area of two ends

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What is volume?

The amount of space occupied by an object is called its volume.

Cubic units are used to measure the volume. For example m3, cm3, in3, ft3 etc.

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Volume of Rectangular Prism

Prism is a 3D figure. The volume of a rectangular prism is given

by the formula: Volume = l × b × h Where l is the length of the rectangular prism. b is the width of the rectangular prism. h is the height of the rectangular prism.

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Practice

Example 1: Find the volume of the rectangular prism whose length is 12 cm, width 6 cm and height 8cm.

Solution: Volume = l × b × h Volume = 12 × 6 × 8 Volume = 576 cm3

The volume of the rectangular prism is 576 cm3.

Volume = l x b x h

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Practice

Example 2: Find the volume of the rectangular prism whose length is 6 in, width 6 in and height 4 in.

Solution: Volume = l × b × h Volume = 6 × 6 × 4 Volume = 144 in3

The volume of the rectangular prism is 144 in3.

Volume = l x b x h

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Volume of Cylinder

Cylinder is a 3D figure. The volume of a cylinder is given by the

formula: Volume = r2h Where r is the radius of the base of the cylinder. h is the height of the rectangular prism. and pi = 3.14.

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Practice

Example 3: Find the volume of the cylinder whose radius is 10 cm and height 6cm.

Solution: Volume = r2h Volume = 3.14 × 102 × 6 Volume = 1884 cm3

The volume of the cylinder is 1884 cm3.

Volume = r2h

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Practice

Example 4: Find the volume of the cylinder whose diameter is 22 cm and height 14 cm.

Solution: Radius r = Diameter/2 = 22/2 = 11 cm Volume = r2h Volume = 3.14 × 112 × 14 Volume = 5319.6 cm3

The volume of the cylinder is 5319.6 cm3.

Volume = r2h

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Your Turn

Find the volume of the rectangular prism whose:

1. l=5 cm, b = 3 cm, h = 4 cm Answer= 60 cm3

2. l=4 in, b = 3 in, h = 5 in Answer= 60 in3

3. l=12 cm, b = 2 cm, h = 7cm Answer= 168 cm3

4. l=10 m, b = 5 m, h = 5 m Answer=250 m3

5. l=5 km, b = 5 km, h = 11km Answer= 275 km3

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Your Turn

Find the volume of the cylinder whose:

6. r = 5 cm, h = 4 cm Answer= 314 cm3

7. r = 10 in, h = 2 in Answer= 628 in3

8. r = 1 km, h = 5 km Answer= 15.7 m3

9. r = 1 m, h = 1 m Answer= 3.14 m3

10. r = 2 cm, h = 2 cm Answer= 15.12cm3

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Q1: Find the length of the rectangular prism whose area is 980 cm3, width is 10cm and height is 7 cm.

Solution: Given that b = 10 cm, Area = 980 cm3 and h =

7cm.

Volume = L x b x h 980 = L x 10 x 7 After simplification we will get 980 = 70L Divide both the sides by 70, we will get L = 14 cm The length of rectangular prism is 14 cm.

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Q2: Find the height of the cylinder whose area is 314 cm3, and radius is 10 cm.

Solution: Given that Area = 314 cm3 and r = 10 cm

Volume = (radius)2x height 314 = 3.14 x (10)2x h After simplification we will get 314 = 3.14 x 100 x h 314 = 314h Divide both the sides by 314, we will get h = 1 cm The length of cylinder is 1 cm.

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Q3: A match box measures 4cm by 2 cm by 2 cm. What will be the volume of the a packet containing a maximum of 12 such boxes?

Solution: First we will find the volume of one match box.

Volume of one match box = 4 x 2 x 2 Volume of one match box = 16 Now volume of one packet is equal to the volume of

12 match boxes. Volume of one packet = Volume of 12 match boxes Volume of one packet = 12 X 16 = 168 The volume of one packet is 168 cm3.

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Let Us Review

The amount of space occupied by an object is called its volume.

The volume of a rectangular prism is given by the formula:

Volume = length × width × height

The volume of a cylinder is given by the formula:

Volume = π(radius)2x height

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You Had a Great Lesson Today!

Be sure to practice what you have learned today