Question:
Case Study - 3: A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative cylindrical pool where it is recycled. The diameter of spherical ball is 21 cm. Cylindrical pool - Outer diameter is 50 cm and inner diameter is 40 cm. Height of solid base is 14 cm. Height of water filled is 7 cm. Observe the figure and answer the following questions :
38(i)
Determine the total height of the fountain.
Case Study - 3: A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative cylindrical pool where it is recycled. The diameter of spherical ball is 21 cm. Cylindrical pool - Outer diameter is 50 cm and inner diameter is 40 cm. Height of solid base is 14 cm. Height of water filled is 7 cm. Observe the figure and answer the following questions :
38(i) Determine the total height of the fountain.
38(i) Determine the total height of the fountain.
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Make sure to read the diagram carefully to determine where the ball sits.
Since the ball rests directly on top of the solid base, the water height of 7 cm does not add to the structure's physical height, as the water level is below the top of the ball.
Since the ball rests directly on top of the solid base, the water height of 7 cm does not add to the structure's physical height, as the water level is below the top of the ball.
Updated On: Jul 7, 2026
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Solution and Explanation
Step 1: Understanding the Question:
This case study is from "Surface Areas and Volumes".
We are given a model of a fountain made of a spherical ball sitting on top of a solid cylindrical base inside a pool.
We need to determine the total height of the fountain structure.
Step 2: Key Formula or Approach:
From the given description and figure:
1. The cylindrical pool has a solid base of height $14\text{ cm}$.
2. The spherical ball has a diameter of $21\text{ cm}$ and rests on top of this solid base.
3. Therefore, the total height of the fountain is the sum of the height of the solid base and the diameter of the ball.
Step 3: Detailed Explanation:
• Identify the vertical components of the fountain:
- Height of the solid base of the cylindrical pool $= 14\text{ cm}$
- Diameter of the spherical ball $= 21\text{ cm}$
• Calculate the total height:
\[ \text{Total Height} = \text{Height of solid base} + \text{Diameter of spherical ball} \] \[ \text{Total Height} = 14 + 21 = 35\text{ cm} \]
Step 4: Final Answer:
The total height of the fountain is $35$ cm.
This case study is from "Surface Areas and Volumes".
We are given a model of a fountain made of a spherical ball sitting on top of a solid cylindrical base inside a pool.
We need to determine the total height of the fountain structure.
Step 2: Key Formula or Approach:
From the given description and figure:
1. The cylindrical pool has a solid base of height $14\text{ cm}$.
2. The spherical ball has a diameter of $21\text{ cm}$ and rests on top of this solid base.
3. Therefore, the total height of the fountain is the sum of the height of the solid base and the diameter of the ball.
Step 3: Detailed Explanation:
• Identify the vertical components of the fountain:
- Height of the solid base of the cylindrical pool $= 14\text{ cm}$
- Diameter of the spherical ball $= 21\text{ cm}$
• Calculate the total height:
\[ \text{Total Height} = \text{Height of solid base} + \text{Diameter of spherical ball} \] \[ \text{Total Height} = 14 + 21 = 35\text{ cm} \]
Step 4: Final Answer:
The total height of the fountain is $35$ cm.
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