Question:
There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylindrical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions:
36(i)
What is the total height of a mushroom ?
There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylindrical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions:
36(i) What is the total height of a mushroom ?
36(i) What is the total height of a mushroom ?
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Always remember that a hemisphere of radius \(R\) has a depth (vertical height) of exactly \(R\). This is a crucial concept when dealing with composite solids.
Updated On: Jun 25, 2026
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Correct Answer: 5
Solution and Explanation
Step 1: Understanding the Question:
We are given a composite solid representing a mushroom:
- An upper hemispherical cap with radius \(R = 3\text{ cm}\).
- A lower cylindrical stem with height \(h = 2\text{ cm}\) and diameter \(d = 1.4\text{ cm}\).
We need to find the total vertical height of this solid mushroom.
Step 2: Key Formula or Approach: 1. The vertical height of a hemisphere is equal to its radius, \(R\).
2. The height of the cylindrical stem is \(h\).
3. Therefore:
\[ \text{Total Height} = \text{Radius of hemispherical cap} + \text{Height of cylindrical stem} \]
Step 3: Detailed Explanation:
• Identify the vertical height of each component from the given details:
- Height of hemispherical cap, \(H_{\text{cap}} = R = 3\text{ cm}\)
- Height of cylindrical stem, \(h = 2\text{ cm}\)
• Add these heights together to get the total height of the mushroom:
\[ H_{\text{total}} = 3 + 2 = 5\text{ cm} \]
Step 4: Final Answer:
The total height of the mushroom is 5 cm.
We are given a composite solid representing a mushroom:
- An upper hemispherical cap with radius \(R = 3\text{ cm}\).
- A lower cylindrical stem with height \(h = 2\text{ cm}\) and diameter \(d = 1.4\text{ cm}\).
We need to find the total vertical height of this solid mushroom.
Step 2: Key Formula or Approach: 1. The vertical height of a hemisphere is equal to its radius, \(R\).
2. The height of the cylindrical stem is \(h\).
3. Therefore:
\[ \text{Total Height} = \text{Radius of hemispherical cap} + \text{Height of cylindrical stem} \]
Step 3: Detailed Explanation:
• Identify the vertical height of each component from the given details:
- Height of hemispherical cap, \(H_{\text{cap}} = R = 3\text{ cm}\)
- Height of cylindrical stem, \(h = 2\text{ cm}\)
• Add these heights together to get the total height of the mushroom:
\[ H_{\text{total}} = 3 + 2 = 5\text{ cm} \]
Step 4: Final Answer:
The total height of the mushroom is 5 cm.
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