To solve this problem, we need to find the total volume of the shape shown. The shape is made of two parts:
1. A cone (the pointed part at the bottom).
2. A hemisphere (the half-sphere on top).
We’ll calculate the volume of each part separately and then add them together.
---
Step 1: Find the radius
The diameter of the circular base is given as 6 cm.
So, the radius = 6 ÷ 2 =
3 cm
---
Step 2: Volume of the cone
Formula for volume of a cone:
> V_cone = (1/3) × π × r² × h
Where:
- r = 3 cm
- h = 10 cm
Plug in the numbers:
V_cone = (1/3) × π × (3)² × 10
= (1/3) × π × 9 × 10
= (1/3) × 90 × π
= 30π cm³
---
Step 3: Volume of the hemisphere
Formula for volume of a full sphere:
> V_sphere = (4/3) × π × r³
Since it’s a hemisphere (half a sphere), we take half of that:
> V_hemisphere = (2/3) × π × r³
Plug in r = 3 cm:
V_hemisphere = (2/3) × π × (3)³
= (2/3) × π × 27
= (54/3) × π
= 18π cm³
---
Step 4: Total volume
Add the two volumes:
Total = V_cone + V_hemisphere
= 30π + 18π
= 48π cm³
If you want a numerical value, use π ≈ 3.14:
48 × 3.14 = 150.72 cm³
But since the question doesn’t specify, leaving it in terms of π is exact and often preferred in math problems.
---
Final Answer:
48π cm³
Parent Tip: Review the logic above to help your child master the concept of composite figure volume worksheet.
