Grade 8 Surface area 1 CONFIDENTIAL
The surface area of a rectangular solid is expressed in square units. The surface area of a solid figure is the sum of the areas of all faces of the figure. An area of study closely related to solid geometry is nets of a solid. Imagine making cuts along some edges of a solid and opening it up to form a plane figure. The plane figure is called the net of the solid. The surface area of a rectangular solid is expressed in square units.
Surface Area of solid figures In general, Surface Area of solid figures = 2 x area of the base +perimeter of the base x height If, B = area of the base P = perimeter of the base h = height SA = Surface Area Then, SA = 2B +Ph
If s is the length of one of its sides, then Cubes A cube is a three-dimensional figure with all edges of the same length. s s If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2
Rectangular prism h h w w l l SA = 2B + Ph SA = 2(lw) + (2l + 2w)h = 2(lw + lh + wh)
Let us do some practice problems!
1) What is the surface area of the cube with length of sides = 7 cm. CONFIDENTIAL 7
2) What is the surface area of the given rectangular prism. 5.5 cm 4 cm 7cm 152 cm2 177 cm2 156 cm2 158 cm2 8 CONFIDENTIAL
3) What is the surface area of the given rectangular prism? 8 4 7 266 cm2 258 cm2 232 cm2 368 cm2 CONFIDENTIAL 9
4) This net can be folded on the dashed lines to make a box 4) This net can be folded on the dashed lines to make a box. What is the surface area of the box? 306 in2. 370 in2. 360 in2. 350 in2. CONFIDENTIAL 10
5) Gina has a sheet of cardboard that measures 9 feet by 6 feet 5) Gina has a sheet of cardboard that measures 9 feet by 6 feet. She uses scissors and tape to make the entire sheet of cardboard into a closed box that is a perfect cube. What is the surface area of the box? 81 feet2 63 feet2 45 feet2 54 feet2 CONFIDENTIAL 11
6) How many unit cubes would it take to fill the box with an area of 10 square feet? CONFIDENTIAL 12
7) The rectangular prism at the right is made from centimeter cubes 7) The rectangular prism at the right is made from centimeter cubes. What is the surface area of the prism? 88 unit2 77 unit2 66 unit2 76 unit2 CONFIDENTIAL 13
8) What is the total surface area of the box, including the bottom and the top? 405 unit2 408 unit2 406 unit2 409 unit2 CONFIDENTIAL 14
9) What is the surface area of the given box? 336 cm2 346 cm2 326 cm2 376 cm2 CONFIDENTIAL 15
10) What is the surface area of the given box? 82 cm2 72 cm2 92 cm2 102 cm2 CONFIDENTIAL 16
Assessment
1) The surface area of a cube is 24 ft2. Find the length of each edge. CONFIDENTIAL 18
2) What is the length of each edge of the box that is a perfect cube with area 54 units2? CONFIDENTIAL 19
3) What is the surface area of the given Regular square prism? 8 11 470 unit2 480 unit2 490 unit2 580 unit2 CONFIDENTIAL 20
4) Bill has a sheet of cardboard with an area of 10 square feet 4) Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area, and the two ends have the same area. The area of each of the four equal sides is twice the area of each end. What is the area of each face of Bill’s box? 2 unit2; 1 unit2 3 unit2; 1.5 unit2 4 unit2; 2 unit2 5 unit2; 2.5 unit2 CONFIDENTIAL 21
5) What is the surface area of the given Regular square pyramid? 180 unit2 150 unit2 146 unit2 136 unit2 CONFIDENTIAL 22
6) What is the surface area of the given square pyramid? 26 yd2 22 yd2 24 yd2 28 yd2 CONFIDENTIAL 23
7) What is the surface area of the given rectangular pyramid? 64 in2 56 in2 45 in2 74 in2 CONFIDENTIAL 24
8) What is the surface area of the given rectangular pyramid? CONFIDENTIAL 25
9) What is the surface area of the given rectangular pyramid? 92 yd2 94 yd2 96 yd2 98 yd2 CONFIDENTIAL 26
10) What is the surface area of the given rectangular pyramid? 592 cm2 564 cm2 594 cm2 565 cm2 CONFIDENTIAL 27
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