Curved Solid Geometry Challenges

1. A cylinder with a radius of 5 cm and a height of 10 cm is combined with a hemisphere of the same radius. Calculate the total volume of the combined solid.

• 1047.2 cm³

• 1234.6 cm³

• 785.4 cm³

• 942.5 cm³

2. Determine the surface area of the combined solid from question 1, including both the curved and flat surfaces.

• Total Surface Area = Curved Surface Area of Cylinder + Area of Base of Cylinder

• Total Surface Area = Curved Surface Area of Cylinder + Flat Surface Area of Hemisphere

• Total Surface Area = Curved Surface Area of Hemisphere + Area of Base of Cylinder

• Total Surface Area = Curved Surface Area of Cylinder + Curved Surface Area of Hemisphere + Area of Base of Hemisphere

3. A water tank is shaped like a cone with a radius of 4 m and a height of 9 m. If the tank is filled to a height of 6 m, calculate the volume of water in the tank.

• 25.00 m³

• 8.50 m³

• 12.34 m³

• 16.76 m³

4. A sphere with a radius of 3 m is placed inside a cylinder with a height of 10 m and a radius of 4 m. Calculate the volume of the space inside the cylinder that is not occupied by the sphere.

• 124π m³

• 150π m³

• 100π m³

• 80π m³

5. A decorative garden is designed in the shape of a half-cylinder with a radius of 2 m and a length of 5 m. Calculate the total surface area of the garden, including the base.

• 60.00 m²

• 69.08 m²

• 78.54 m²

• 50.24 m²