A rectangular solid is also called a rectangular prism or cuboid.
The volume is found using the formula:
The total surface area (TSA) of a cuboid is the sum of the areas of its six faces.
Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm.
TSA = 2 (lw+wh+hl)
TSA = 2 (8⋅6+6⋅5+5⋅8) = 2(48+30+40) = 236 cm2
So, the total surface area of this cuboid is 236 cm2
We want to find the volume of this cuboid in cm3
To find the volume we mulptiply the sides.
V=3∙4∙7 = 84 cm3
- A cuboid has lateral surface 199 cm2 . The base has sides 23 cm and 14 cm long. Calculate the height. Solution
- A cuboid has its height equal to the diagonal of the base. The sum of the two sides of the base is 21 cm and one is 3/4 of the other. Calculate the total surface area.
- The diagonal of a cuboid is 117 cm the base has sides 36 cm and 27 cm long. Calculate the volume and the total surface area.
- A cuboid has the perimeter of the base equal to 84 dm and one side is 3/4 of the other. The height is 40 dm long. Calculate the total surface area.
- The sum of two sides of a cuboid is 14 cm and one side is 4/3 of the other. Knowing that the total surface area is 768 cm2 , calculate the third dimension of the cuboid.
- The difference between two sides of a cuboid is 14 cm and one side 15/8 of the other. The third side (height) is 33 cm long. A second cuboid has a squared base with 121 cm2 area and has the same lateral area of the first one. Calculate the third side.
- A cuboid has two sides 13 cm and 15 cm long. The total surface area is 950 cm2 . Calculate the volume. Solution
- The squared base of a cuboid is 576 cm2 . The height of the cuboid is 1/12 of the perimeter of the base. Calculate lateral surface and volume.
- The volume of a cuboid is 108 cm3 and two sides are 4.5 cm and 6 cm long. Calculate the diagonal and the total surface area of the cuboid.
- The volume of a cuboid is 1768 cm3 . The sum and the difference between two sides are 30 cm and 4 cm. Calculate the lenght of the third side.
- The perimeter of the base of a cuboid is 66 cm and one side is 6/5 of the other. The volume is 2.97dm3 . Calculate the lenght of the third side.