Math: Volume and Surface Area
Finding space inside and outside 3D figures
Math: Volume and Surface Area
Finding space inside and outside 3D figures
Math - Grade 6-8
- 1
A cube has side length 4 cm. What is its volume?
For a cube, multiply the side length by itself three times.
The volume is 64 cubic centimeters because 4 x 4 x 4 = 64. - 2
A rectangular prism has length 8 m, width 3 m, and height 5 m. What is its volume?
The volume is 120 cubic meters because 8 x 3 x 5 = 120. - 3
A cube has side length 6 in. What is its surface area?
Surface area of a cube is 6 times the area of one face.
The surface area is 216 square inches because a cube has 6 equal faces and 6 x 6^2 = 6 x 36 = 216. - 4
A rectangular prism has length 7 cm, width 2 cm, and height 4 cm. What is its surface area?
The surface area is 100 square centimeters because 2(7 x 2 + 7 x 4 + 2 x 4) = 2(14 + 28 + 8) = 100. - 5
A fish tank is shaped like a rectangular prism with dimensions 10 in by 6 in by 8 in. How much water can it hold if filled to the top?
Use volume for the amount a container can hold.
The tank can hold 480 cubic inches of water because 10 x 6 x 8 = 480. - 6
A gift box measures 9 cm by 5 cm by 3 cm. How much cardboard is needed to cover the outside of the box completely?
The box needs 174 square centimeters of cardboard because 2(9 x 5 + 9 x 3 + 5 x 3) = 2(45 + 27 + 15) = 174. - 7
A storage bin has a base area of 24 square feet and a height of 5 feet. What is its volume?
You can use V = Bh when the base area is given.
The volume is 120 cubic feet because volume equals base area times height, so 24 x 5 = 120. - 8
A rectangular prism has volume 96 cubic centimeters, length 8 cm, and width 3 cm. What is its height?
The height is 4 centimeters because 96 = 8 x 3 x h, so 96 = 24h and h = 4. - 9
A cube has a volume of 125 cubic meters. What is the side length of the cube?
Think of a number that multiplies by itself three times to make 125.
The side length is 5 meters because 5 x 5 x 5 = 125. - 10
Find the surface area of a rectangular prism with length 12 ft, width 4 ft, and height 2 ft.
The surface area is 160 square feet because 2(12 x 4 + 12 x 2 + 4 x 2) = 2(48 + 24 + 8) = 160. - 11
A cereal box is 10 in tall, 3 in wide, and 2 in deep. Find both its volume and surface area.
First find the space inside, then find the total area of all six faces.
The volume is 60 cubic inches because 10 x 3 x 2 = 60. The surface area is 112 square inches because 2(10 x 3 + 10 x 2 + 3 x 2) = 2(30 + 20 + 6) = 112. - 12
A cube-shaped container has side length 9 cm. How many square centimeters of material are needed to make the container if it is closed on all sides?
It needs 486 square centimeters of material because the surface area of a cube is 6s^2, and 6 x 9^2 = 6 x 81 = 486. - 13
A rectangular prism has dimensions 5 yd by 4 yd by 3 yd. If the height is doubled, what is the new volume?
Replace the original height with double its value before multiplying.
The new volume is 120 cubic yards because the new height is 6 yards, and 5 x 4 x 6 = 120. - 14
A prism has a base area of 18 square inches and a height of 7 inches. What is its volume?
The volume is 126 cubic inches because 18 x 7 = 126. - 15
A rectangular prism has surface area 94 square centimeters, length 5 cm, width 4 cm, and height h. Find h.
Write the surface area formula and solve the equation step by step.
The height is 3 centimeters because 94 = 2(5 x 4 + 5h + 4h). This gives 94 = 2(20 + 9h), so 94 = 40 + 18h, then 54 = 18h, and h = 3.