 # Confidential 2 Warm Up Find the Surface area of each rectangular Prism to the nearest tenth 5.5cm 2.3cm 10cm 1. 2. 7.8 in. 6.2 in. 5.4 in. 181.3cm 2 247.9.

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Confidential 2 Warm Up Find the Surface area of each rectangular Prism to the nearest tenth 5.5cm 2.3cm 10cm 1. 2. 7.8 in. 6.2 in. 5.4 in. 181.3cm 2 247.9 in 2

Confidential 3 Warm Up Find the surface area of Cylinders: 4. r = 6mm, h = 10 mm 603.2mm 2 5. r = 3.5 ft, h = 24 ft 604.8ft 2 3. Write the formula for the surface area of a Cube in which each edge measures x units. Surface area = 6x 2

Confidential 4 Surface Area of a Prism The surface area of a prism is the sum of the areas of all the sides of the prism. The formula for the surface area of a prism therefore depends on the type of prism. Surface Area of a Cylinder The surface area of a cylinder is the sum of the areas of the two bases and the lateral face of the cylinder. surface area of a cylinder = 2*  r 2 + 2  rh Lets review what we have learned in the last lesson

Confidential 5 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

Confidential 6 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 m 3, cm 3, in 3, ft 3 etc.

Confidential 7 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.

Confidential 8 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 cm 3 The volume of the rectangular prism is 576 cm 3. Volume = l x b x h

Confidential 9 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 in 3 The volume of the rectangular prism is 144 in 3. Volume = l x b x h

Confidential 10 Volume of Cylinder Cylinder is a 3D figure. The volume of a cylinder is given by the formula: Volume = r 2 h Where r is the radius of the base of the cylinder. h is the height of the rectangular prism. and pi = 3.14.

Confidential 11 Practice Example 3: Find the volume of the cylinder whose radius is 10 cm and height 6cm. Solution: Volume = r 2 h Volume = 3.14 × 10 2 × 6 Volume = 1884 cm 3 The volume of the cylinder is 1884 cm 3. Volume = r 2 h

Confidential 12 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 = r 2 h Volume = 3.14 × 11 2 × 14 Volume = 5319.6 cm 3 The volume of the cylinder is 5319.6 cm 3. Volume = r 2 h

Confidential 13 Your Turn Find the volume of the rectangular prism whose: 1. l=5 cm, b = 3 cm, h = 4 cm Answer= 60 cm 3 2. l=4 in, b = 3 in, h = 5 in Answer= 60 in 3 3. l=12 cm, b = 2 cm, h = 7cm Answer= 168 cm 3 4. l=10 m, b = 5 m, h = 5 m Answer=250 m 3 5. l=5 km, b = 5 km, h = 11km Answer= 275 km 3

Confidential 14 Your Turn Find the volume of the cylinder whose: 6. r = 5 cm, h = 4 cm Answer= 314 cm 3 7. r = 10 in, h = 2 in Answer= 628 in 3 8. r = 1 km, h = 5 km Answer= 15.7 m 3 9. r = 1 m, h = 1 m Answer= 3.14 m 3 10. r = 2 cm, h = 2 cm Answer= 15.12cm 3

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Confidential 17 Q1: Find the length of the rectangular prism whose area is 980 cm 3, width is 10cm and height is 7 cm. Solution: Given that b = 10 cm, Area = 980 cm 3 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.

Confidential 18 Q2: Find the height of the cylinder whose area is 314 cm 3, and radius is 10 cm. Solution: Given that Area = 314 cm 3 and r = 10 cm Volume = (radius) 2 x height 314 = 3.14 x (10) 2 x 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.

Confidential 19 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 cm 3.

Confidential 20 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) 2 x height

Confidential 21 You Had a Great Lesson Today! Be sure to practice what you have learned today

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