Answer:
The volume of liquid that will fill the bowl of the glass is approximately 178.82 cm³
Step-by-step explanation:
The given dimensions of the bowl are;
The shape of the bowl containing the liquid = A cone
The base length of the triangular cross-section of the cone = The diameter of the cone, d = 6 cm
The slant height of the triangular cross-section of the cone = The slant height of the cone, l = 7 cm
Therefore, the height of the cone, h = √(l² - (d/2)²)
∴ h = √(7² - (6/2)²) = 2·√10
The height of the cone, h = 2·√10 cm
The volume of a cone, V = (1/3) × Base area, A × Height, h
V = A × h
The base area of the cone, A = π × (d/2)²
A = π×(6/2 cm)² = 9·π cm²
By plugging in the values
V = A × h
∴ V = 9·π cm² × 2·√10 cm ≈ 178.82 cm³
The volume of the cone = The volume of liquid that will (can) fill the bowl of the glass, V ≈ 178.82 cm³.
