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100
A triangular prism has a length of 16 cm, a width of 8 cm, and a height of 6 cm. Find the surface area of the figure. 
Area of triangle bases: 8 x 6 / 2 = 24 x 2 bases = 48

Area of lateral faces: 16 x 6 = 96 x 3 faces = 288

Total surface area: 48 + 288 = 336 cm^2. 

100
A rectangular prism has a length of 8 1/2 feet, width of 6 1/2 feet, and height of 12 1/2 feet. What is the volume of the prism?
V = L x W x H

V = 8.5 x 6.5 x 12.5 = 690.625 or 690 5/8 ft^3. 

100
A rectangular prism has a length of 3 1/2 inches, a width of 2 1/2 inches, and a height of 2 inches. What is the volume of the shape?
Volume = L x W x H

Volume = 3 1/2 x 2 1/2 x 2 = 17.5 inches^3

200
Emily has a decorative box shaped like a cube with a height of 5 inches. What is the surface area of the box? 
Area of 1 face: 5 x 5 = 25

25 x 6 congruent faces = 150 inches^2

200
A water irrigation tank is shaped like a cube and has a side length of 2.5 feet. How many cubic feet of water are needed to completely fill the tank?
L = 2.5

W = 2.5

H = 2.5

V = L x W x H = 2.5 x 2.5 x 2.5 = 15.625 or 15 5/8 feet^3

200
A cereal box is 8 inches long, 10 inches tall, and 3 inches wide. What is the surface area? 
Area of the bases: 8 x 3 = 24 x 2 bases = 48

Area of front and back sides: 8 x 10 = 80 x 2 faces = 160

Area of left and right sides: 3 x 10 = 30 x 2 faces = 60 

Total surface area: 48 + 160 + 60 = 268 inches^2

300
The caps on the tops of staircase posts are shaped like square pyramids. The side length of the base of each cap is 4 inches. The height of the face of each cap is 5 inches. What is the surface area of the caps for two posts? 
Area of a triangle: A = b x h / 2

Lateral area: 4 x 5 = 20 / 2 = 10 x (4 faces) = 40 in^2

Area of a square: A = b x h

Base area: 4 x 4 = 16 in^2

Surface area of 1 cap: 56 in^2, of 2 caps: 112 in^2

300

The outside of an aquarium tank is 50 cm long, 50 cm wide, and 30 cm high. It is open at the top. The glass used to make the tank is 1 cm thick. How much water can the tank hold? 

L = 50 - 2 = 48

W = 50 - 2 = 48

H = 30 - 1 = 29

V = L x W x H = 48 x 48 x 29 = 66, 816 cm^3

300
A square pyramid has a base side length of 12 inches and a height of 7 inches. What is the lateral area of the figure? 
*Does not include the base area.


Lateral area = 12 x 7 /2 = 42 x 4 faces = 168 inches^2.

400
The Pyramid Arena is located in Memphis, Tennessee. It is in the shape of a square pyramid, and the lateral faces are made almost completely out of glass. The base has a side length of about 600 feet and the lateral faces have a height of about 440 feet. What is the total surface area of the Pyramid Arena?
SA = Area of lateral faces + Area of base

Lateral faces = (600 x 440) / 2 = 132,000 x 4 sides = 528,000 feet^2

Base = 600 x 600 = 360,000 feet^2

SA = 528,000 + 360,000 = 888,000 feet^2

400
Arnie keeps his pet snake in an open-topped glass cage. The outside of the cage is 73 cm long, 60 cm wide, and 38 cm high. The glass used to make the cage is 0.5 cm thick. What is the inside volume of the cage? 
L = 73 - (0.5 + 0.5) = 72

W = 60 - 1 = 59

H = 38 - 0.5 = 37.5

V = L x W x H = 72 x 59 x 37.5 = 159, 300 cm^3

400
Find the volume of a stove that is 3 feet wide, 4 feet long, and 4 feet high. 
V = L x W X H

V = 4 x 3 x 4 = 48 feet^3. 

500
Stella needs to send a package in the shape of a rectangular prism. The box has a length of 2 1/2 feet, a width of 1 1/2 feet, and a height of 4 feet. Stella needs to cover the box with wrapping paper. How much paper will she need?
Area of 2 bases: 1 1/2 x 4 = 6 x 2 bases = 12

Area of front and back: 2 1/2 x 4 = 10 x 2 faces = 20

Area of top and bottom: 2 1/2 x 1 1/2 = 3 3/4 x 2 faces = 7 1/2

Total surface area: 12 + 20 + 7 1/2 = 39 1/2 feet^2 of wrapping paper. 

500
The area of the base of a prism is 9 in^2. The height of the prism is 2 1/4 in. What is the volume of the prism?
V = Area of one base x height

V = 9 x 2 1/4 = 20 1/4 in^2

500
The area of the base of a block of concrete is 12 feet^2. If the height of the block is 4 feet, what is the volume of the concrete? 
V = B x h 

V = 12 x 4 = 48 feet^3.