Volume Calculation for 3D Objects
To arrange the objects in descending order of volume, we first calculate the volume of each:
Cuboid Volume
The dimensions of the cuboid are 10 cm, 8 cm, and 6 cm.
Volume$_{cuboid} = \text{length} \times \text{width} \times \text{height}$
Volume$_{cuboid} = 10 \text{ cm} \times 8 \text{ cm} \times 6 \text{ cm} = 480 \text{ cm}^3$
Cube Volume
The side length of the cube is 8 cm.
Volume$_{cube} = \text{side}^3$
Volume$_{cube} = (8 \text{ cm})^3 = 512 \text{ cm}^3$
Cylinder Volume
The base radius ($r$) is 7 cm and the height ($h$) is 7 cm. Using $\pi \approx \frac{22}{7}$.
Volume$_{cylinder} = \pi r^2 h$
Volume$_{cylinder} = \frac{22}{7} \times (7 \text{ cm})^2 \times 7 \text{ cm}$
Volume$_{cylinder} = \frac{22}{7} \times 49 \text{ cm}^2 \times 7 \text{ cm} = 22 \times 49 \text{ cm}^3 = 1078 \text{ cm}^3$
Sphere Volume
The radius ($r$) of the sphere is 7 cm. Using $\pi \approx \frac{22}{7}$.
Volume$_{sphere} = \frac{4}{3} \pi r^3$
Volume$_{sphere} = \frac{4}{3} \times \frac{22}{7} \times (7 \text{ cm})^3$
Volume$_{sphere} = \frac{4}{3} \times \frac{22}{7} \times 343 \text{ cm}^3 = \frac{4}{3} \times 22 \times 49 \text{ cm}^3 = \frac{4312}{3} \text{ cm}^3 \approx 1437.33 \text{ cm}^3$
Ordering Objects by Volume
Comparing the calculated volumes:
- Sphere (iv): $\approx 1437.33 \text{ cm}^3$
- Cylinder (iii): $1078 \text{ cm}^3$
- Cube (ii): $512 \text{ cm}^3$
- Cuboid (i): $480 \text{ cm}^3$
Arranging these in descending order (largest to smallest volume) gives:
(iv), (iii), (ii), (i)
