Unit Exam Surface Area of Common Solids Solutions.

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Presentation transcript:

Unit Exam Surface Area of Common Solids Solutions

The radius of the cone shown is 3 units and it has a hieght of 4 units The radius of the cone shown is 3 units and it has a hieght of 4 units. Calculate the surface area of the cone. s 4 S.A = pr2 +prs =(3.141)(3)2 + (3.141)(3)(5) =(3.141)(9) + (3.141)(3)(5) =28.269 + (3.141)(3)(5) =28.269 + (9.423)(5) =28.269 + 47.115 =75.384 3 To Find the Slant a2 + b2 = s2 32 + 42 = s2 9 + 16 = s2 25 = s2 √25 = s 5 = s Surface Area is 75.384 units2

The rectangular parallelepiped shown has a length of ten inches, a width of four inches and a height of five inches. Calculate the rectangular prism's surface area. 4 5 4 10 S.A. = 2(l * w) + 2 (w * h) + 2(h * l) = 2(10 * 4) + 2(4 * 5) + 2(5 * 10) = 2(40) + 2(20) + 2(50) = 80 + 40 + 100 = 220 Surface Area is 220 inches2

The cylinder shown has a radius of one meter and a length of ten meters. Determine the surface area of the cylinder. 10 1 S.A. = 2pr2 + pDh = 2(3.141)(1)2 + (3.141)(2)(10) = 2(3.141)(1) + (3.141)(2)(10) = 2(3.141) + (3.141)(2)(10) = 6.282 + (3.141)(2)(10) = 6.282 + (6.282)(10) = 6.282 + 62.82 = 69.102 Surface Area ia 69.102 meters2 The diameter is twice the radius so D = 2

Surface Area is 50.75 centimeters2 The pentagonal pyramid shown has a base with an apothem of two centimeters and a side of 2.9 centimeters. Each trianglular lateral face has an altitude, drawn from top vertex to the base, of five centimeters. What is the surface area of the pyramid? 5 2 2.9 S.A. = ½ap + 5(½bh) = ½(2)(14.5) + 5(½)(2.9)(5) = (1)(14.5) + 5(½)(2.9)(5) = (14.5) + 5(½)(2.9)(5) = 14.5 + (2.5)(2.9)(5) = 14.5 + (7.25)(5) = 14.5 + 36.25 = 50.75 Surface Area is 50.75 centimeters2 Perimeter 2.9 x 5 = 14.5

Surface area is 125,640 kilometers2 The sphere shown has a radius of 100 kilometers. Calculate the surface area of the sphere. 100 100 S.A. = 4πr2 = 4(3.141)(100)2 = 4(3.141)(10000) = (12.564)(10000) = 125,640 Surface area is 125,640 kilometers2

Name the solids, or solid formed by the net, shown. Dodecahedron Octahedron Icosahedron Square Base Pyramid Frustum