CONFIDENTIAL 1

Grade 8 Grade 8

Surface area 1Surface area 1

Surface area

The surface area of a solid figure is the sum of the areas of all faces of the figure.

The surface area of a rectangular solid is expressed in square units.

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.

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

Cubes

A cube is a three-dimensional figure with all edges of the same length.

If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2

s

sss s

s

s s

s

Rectangular prism

l w

h

l w

h

SA = 2B + Ph

SA = 2(lw) + (2l + 2w)h = 2(lw + lh + wh)

Let us do some practice problems!

CONFIDENTIAL7

1) What is the surface area of the cube with length of sides = 7 cm.

a) 296 cm2

b) 294 cm2

c) 394 cm2

d) 284 cm2

CONFIDENTIAL8

2) What is the surface area of the given rectangular prism.

a) 152 cm2

b) 177 cm2

c) 156 cm2

d) 158 cm25.5 cm 4 cm

7cm

CONFIDENTIAL 9

3) What is the surface area of the given rectangular prism?

a) 266 cm2

b) 258 cm2

c) 232 cm2

d) 368 cm2

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CONFIDENTIAL 10

4) This net can be folded on the dashed lines to make a box. What is the surface area of the box?

a) 306 in2.b) 370 in2.c) 360 in2.d) 350 in2.

CONFIDENTIAL 11

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?

a) 81 feet2

b) 63 feet2

c) 45 feet2

d) 54 feet2

CONFIDENTIAL 12

6) How many unit cubes would it take to fill the box with an area of 10 square feet?

a) 4 cubesb) 3 cubesc) 2 cubesd) 1 cube

CONFIDENTIAL13

7) The rectangular prism at the right is made from centimeter cubes. What is the surface area of the prism?

a) 88 unit2

b) 77 unit2

c) 66 unit2

d) 76 unit2

CONFIDENTIAL 14

8) What is the total surface area of the box, including the bottom and the top?

a) 405 unit2

b) 408 unit2

c) 406 unit2

d) 409 unit2

CONFIDENTIAL 15

9) What is the surface area of the given box?

a) 336 cm2

b) 346 cm2

c) 326 cm2

d) 376 cm2

CONFIDENTIAL 16

10) What is the surface area of the given box?

a) 82 cm2

b) 72 cm2

c) 92 cm2

d) 102 cm2

Assessment

CONFIDENTIAL18

1) The surface area of a cube is 24 ft2. Find the length of each edge.

a) 4 ftb) 3 ftc) 2 ftd) 1 ft

CONFIDENTIAL 19

2) What is the length of each edge of the box that is a perfect cube with area 54 units2?

a) 2 unitsb) 3 unitsc) 4 unitsd) 5 units

CONFIDENTIAL 20

3) What is the surface area of the given Regular square prism?

a) 470 unit2

b) 480 unit2

c) 490 unit2

d) 580 unit2

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CONFIDENTIAL 21

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?

a) 2 unit2; 1 unit2

b) 3 unit2; 1.5 unit2

c) 4 unit2; 2 unit2

d) 5 unit2; 2.5 unit2

CONFIDENTIAL 22

5) What is the surface area of the given Regular square pyramid?

a) 180 unit2

b) 150 unit2

c) 146 unit2

d) 136 unit2

CONFIDENTIAL 23

6) What is the surface area of the given square pyramid?

a) 26 yd2

b) 22 yd2

c) 24 yd2

d) 28 yd2

CONFIDENTIAL 24

7) What is the surface area of the given rectangular pyramid?

a) 64 in2

b) 56 in2

c) 45 in2

d) 74 in2

CONFIDENTIAL 25

8) What is the surface area of the given rectangular pyramid?

a) 226 ft2

b) 256 ft2

c) 246 ft2

d) 236 ft2

CONFIDENTIAL 26

9) What is the surface area of the given rectangular pyramid?

a) 92 yd2

b) 94 yd2

c) 96 yd2

d) 98 yd2

CONFIDENTIAL 27

10) What is the surface area of the given rectangular pyramid?

a) 592 cm2

b) 564 cm2

c) 594 cm2

d) 565 cm2

You did a great job today!