Determine the ratio of the cone, cylinder, and hemisphere volumes with the same height and circular base. [Answer Limit: 50 words] [UKPSC 2012]
Characteristics of a good paint include: 1. **Color Retention**: It should maintain its hue over time. 2. **Adhesion**: It must adhere well to surfaces. 3. **Quick Drying**: A short drying time is desirable for efficiency. 4. **Water Resistance**: It should withstand moisture and humidity. 5. **WashRead more
Characteristics of a good paint include:
1. **Color Retention**: It should maintain its hue over time.
2. **Adhesion**: It must adhere well to surfaces.
3. **Quick Drying**: A short drying time is desirable for efficiency.
4. **Water Resistance**: It should withstand moisture and humidity.
5. **Washability**: It should be easy to clean without damage.
Components of paint include:
1. **Pigments**: Provide color and opacity; they affect the paint’s durability and UV resistance.
2. **Binders**: Help the paint adhere to surfaces and form a film; examples include acrylics and alkyds.
3. **Solvents**: Liquids that dissolve the binder and control the paint’s viscosity, allowing for smooth application.
4. **Additives**: Enhance specific properties, such as mildew resistance, flow control, or texture.
Together, these components determine the paint’s performance and application.
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For a cone, hemisphere, and cylinder with the same circular base radius 𝑟 r and height ℎ h: Cone volume: 1 3 𝜋 𝑟 2 ℎ 3 1 πr 2 h Hemisphere volume: 2 3 𝜋 𝑟 3 3 2 πr 3 Cylinder volume: 𝜋 𝑟 2 ℎ πr 2 h The ratio of volumes is 1 : 2 : 3 1:2:3.
For a cone, hemisphere, and cylinder with the same circular base radius
𝑟
r and height
ℎ
h:
Cone volume:
1
3
𝜋
𝑟
2
ℎ
3
1
πr
2
h
Hemisphere volume:
2
3
𝜋
𝑟
3
3
2
πr
3
Cylinder volume:
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𝑟
2
ℎ
πr
2
h
The ratio of volumes is
1
:
2
:
3
1:2:3.