FIND THE TOTAL SURFACE AREA OF GIVEN CUBOID OR RECTANGULAR PRISM

Problem 1 :

Solution:

Given, length = 5 cm

Breadth = 3 cm

Height = 4 cm

Total surface area of rectangular prism = 2(lb + bh + lh)

= 2((5×3) + (3×4) + (5×4))

= 2(15 + 12 + 20)

= 2(47)

= 94 cm²

Problem 2 :

Solution:

Given, length = 12 in.

Breadth = 8 in.

Height = 4 in.

Total surface area of rectangular prism = 2(lb + bh + lh)

= 2((12×8) + (8×4) + (12×4))

= 2(96 + 32 + 48)

= 2(176)

= 352 in².

Problem 3 :

Solution:

Given, length = 30 cm

Breadth = 5 cm

Height = 40 cm

Total surface area of rectangular prism = 2(lb + bh + lh)

= 2((30×5) + (5×40) + (30×40))

= 2(150 + 200 + 1200)

= 2(1550)

= 775 cm²

Problem 4 :

Solution:

Given, length = 15 feet

Breadth = 3 feet

Height = 3 feet

Total surface area of rectangular prism = 2(lb + bh + lh)

= 2((15×3) + (3×3) + (15×3))

= 2(45 + 9 + 45)

= 2(99)

= 49.5 feet²

Problem 5 :

Solution:

Given, side = 5 cm

Surface area of cube = 6s²

= 6(5)²

= 6(25)

SA = 150 cm²

Problem 6 :

Find the surface area of a rectangular prism that has a length of 8 inches, a width of 3 inches, and a height of 6 inches.

Solution:

Given, length = 8 inches

Breadth = 3 inches

Height = 6 inches

Total surface area of rectangular prism = 2(lb + bh + lh)

= 2((8×3) + (3×6) + (8×6))

= 2(24 + 18 + 48)

= 2(90)

= 45 inches²

Problem 7 :

A box that is 15 inches wide, 25 inches high, and 2 inches thick is to be wrapped in gift paper. How many square inches of gift paper are needed?

Solution:

Given, wide = 15 inches

Height = 25 inches

Thick = 2 inches

Total surface area of rectangular prism = 2(lb + bh + lh)

= 2((15×25) + (25×2) + (15×2))

= 2(375 + 50 + 30)

= 2(455)

= 227.5 inches²

Hence, 227.5 square inches of gift paper are needed.

Problem 8  :

Find the indicated area for the rectangular prism.

a)  Area of Face A

b)  Area of Face B

c)  Area of Face C

d) Surface area of the prism

Solution :

a)

Area of face A = length x width

length = 6 cm and width = 4 cm

= 6 x 4

= 24 cm²

b)

Area of face B = length x width

length = 6 cm and width = 3 cm

= 6 x 3

= 18 cm²

c)

Area of face C = length x width

length = 3 cm and width = 4 cm

= 3 x 4

= 12 cm²

d) Surface area of prism = 2(Area of face A + area of face C)

= 2(24 + 12)

= 2(36)

= 72 cm²

Problem 9  :

What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches? Explain.

Solution :

Length = 8 inches, width = 8 inches and height = 10 inches

Total surface area of wrapping paper = 2(lw + wh + hl)

= 2(8⋅8 + 8⋅10 + 10⋅8)

= 2(64 + 80 + 80)

= 2(224)

= 448 square inches

Problem 10  :

A public library has an aquarium in the shape of a rectangular prism. The base is 6 feet by 2.5 feet. The height is 4 feet. How many square feet of glass were used to build the aquarium? (The top of the aquarium is open.)

Solution :

Excluding the top, we have 5 sides.

length = 6 feet, width = 2.5 feet and height = 4 feet

Area of front and back = 2(length x height)

= 2(6 x 4)

= 2 x 24

= 48 square feet

Area of bottom face = length x width

= 6 x 2.5

= 15 square feet

Area of side faces = 2(width x height)

= 2(2.5 x 4)

= 2(10)

= 20 square feet

Quantity of glass needed = 48 + 15 + 20

= 83 square feet

Problem 11  :

The material used to make a storage box costs $1.25 per square foot. The boxes have the same volume. How much does a company save by choosing to make 50 of Box 2 instead of 50 of Box 1?

Solution :

Total surface area of box 1 :

Total surface area = 2(lw + wh + hl)

= 2(20⋅6 + 6⋅4 + 4⋅20)

= 2(120 + 24 + 80)

= 2(224)

= 448 square inches

Total surface area of box 2 :

Total surface area = 2(lw + wh + hl)

= 2(15⋅4 + 4⋅8 + 8⋅15)

= 2(60+  32 + 120)

= 2(212)

= 424 square inches

Total cost of Box 1 :

Making 50 boxes = 50 x 448

= 22400 squre inches

Cost per square feet = $1.25

Total cost of 50 boxes = 22400 x 1.25

= $28000

Total cost of Box 2 :

Making 50 boxes = 50 x 424

= 21200 squre inches

Cost per square feet = $1.25

Total cost of 50 boxes = 21200 x 1.25

= $26500

Difference = 28000 - 26500

= $1500