krit.club logo

Measurement - Volume and surface area of cuboids

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

A cuboid (rectangular prism) is a 3D shape with 6 rectangular faces, 12 edges, and 8 vertices.

•

Volume is the amount of 3D space an object occupies, measured in cubic units like cm3cm^3 or m3m^3.

•

Surface Area is the total area of all the outer faces of a 3D object, measured in square units like cm2cm^2 or m2m^2.

•

A cube is a special type of cuboid where the length, width, and height are all equal (l=w=hl = w = h).

•

The net of a cuboid consists of 6 rectangles arranged in a way that they can be folded to form the solid.

📐Formulae

Volume of a cuboid: V=limeswimeshV = l imes w imes h

Total Surface Area of a cuboid: SA=2(lw+lh+wh)SA = 2(lw + lh + wh)

Volume of a cube: V=s3V = s^3 (where ss is the side length)

Total Surface Area of a cube: SA=6s2SA = 6s^2

💡Examples

Problem 1:

Find the volume and total surface area of a cuboid with length 8 cm, width 5 cm, and height 3 cm.

Solution:

Volume = 120 cm3120 \text{ cm}^3, Surface Area = 158 cm2158 \text{ cm}^2

Explanation:

To find the volume, multiply the dimensions: 8×5×3=120 cm38 \times 5 \times 3 = 120 \text{ cm}^3. To find the surface area, use the formula 2(lw+lh+wh)2(lw + lh + wh): 2((8×5)+(8×3)+(5×3))=2(40+24+15)=2(79)=158 cm22( (8 \times 5) + (8 \times 3) + (5 \times 3) ) = 2(40 + 24 + 15) = 2(79) = 158 \text{ cm}^2.

Problem 2:

A cube has a side length of 4 cm. Calculate its volume.

Solution:

Volume = 64 cm364 \text{ cm}^3

Explanation:

Since all sides of a cube are equal, the volume is s×s×ss \times s \times s. Therefore, 4×4×4=64 cm34 \times 4 \times 4 = 64 \text{ cm}^3.

Problem 3:

A cuboid has a volume of 200 cm3200 \text{ cm}^3. If the length is 10 cm and the width is 5 cm, find the height.

Solution:

Height = 4 cm4 \text{ cm}

Explanation:

Using the volume formula V=l×w×hV = l \times w \times h, we substitute the known values: 200=10×5×h200 = 10 \times 5 \times h. This simplifies to 200=50h200 = 50h. Dividing both sides by 50 gives h=4 cmh = 4 \text{ cm}.