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Surface Area and Volume of Prisms & Cylinders

Surface Area and Volume of Prisms & Cylinders. Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder. I. Surface Area of a Prism. Prism – Is a polyhedron with exactly 2 congruent, parallel faces, called bases.

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Surface Area and Volume of Prisms & Cylinders

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  1. Surface Area and Volume of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder.

  2. I. Surface Area of a Prism • Prism – Is a polyhedron with exactly 2 congruent, parallel faces, called bases. • Name it by the shape of its bases. Bases are Rectangles: Lateral Faces – All faces that are not bases. (Sides)

  3. Right Prisms vs Oblique Prisms Oblique Prism – Lateral faces are parallelograms Right Prism – Lateral faces are rectangles.

  4. Total Surface Area = Lateral Area + 2 Base Area • If the base is a regular polygon all 4 rectangles will be congruent • If the base is a non regular polygon you should look at individual rectangles and calculate their areas with A = l•w Lateral Area –

  5. Total Surface Area = Lateral Area + 2 Base Area Base Area – • Rectangle: A = l•w • Triangle: A = ½bh

  6. Ex.1: Find the Surface Area of the rectangular Prism. Lateral Area Left and right rectangles are congruent A = l•w= 3•5 = 15 cm2 Front and back rectangles are congruent A = l•w= 4•5 = 20 cm2 Total = 15+15+20+20 =70 cm2 Area of Bases: A = l•w = 4•3 = 12 cm2 5cm 3cm 4cm SA = LA + BA = 70cm2 + 24cm2 = 94cm2

  7. Ex.2: Find the total surface area of the following triangular prism. 5cm LA = l•w (5 x 12) = 60cm2 (5 x 12) = 60cm2 (6 x 12) = 72cm2 5cm h 4 cm 12cm 6cm 192cm2 BA = ½bh = ½(6)(4) = 12cm2 x 2 24cm2 SA = LA + BA = 192cm2 + 24cm2 = 216cm2

  8. II. Finding Surface Area of a Cylinder Cylinder Has 2 congruent, parallel bases Base → Circle C = 2πr A = πr2 r height r h r

  9. Net of a Cylinder: LA is just a Rectangle! Area of a circle LA = 2rh BA = r2 r Circumference of the circle SA = LA + 2BA

  10. Ex.3: SA of a right cylinder LA = 2rh = 2(6)(9) = 108ft2 = 339.3ft2 6ft Area of Base BA = r2 = (6)2 = 36ft2 9ft x 2 SA = LA + BA = 339.3ft2 + 226.2ft2 = 565.5ft2 = 72ft2 = 226.2 ft2

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