1. Unit Exam
Surface Area of
Common Solids
Solutions

2. 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)
= (3.141)(3)(5)
= (9.423)(5) =
=75.384 3
To Find the Slant
a2 + b2 = s2
= s2
= s2
25 = s2
√25 = s
5 = s
Surface Area is units2

3. 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) =
= 220
Surface Area is 220 inches2

4. 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)
= (3.141)(2)(10)
= (6.282)(10) = =
Surface Area ia meters2
The diameter is twice the radius so D = 2

5. 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)
= (2.5)(2.9)(5)
= (7.25)(5) =
= 50.75
Surface Area is centimeters2
Perimeter
2.9 x 5 = 14.5

6. 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

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