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a solid is in the form of a cylinder withhemispherical ends. the total height of the solid is 19cm and the diameter of the cylinder is 7 cm. find thevolume and surface area of the solid.

1 Answer

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Final answer:

The volume of the solid is 172.01 cm³ and the surface area is 271.60 cm².

Step-by-step explanation:

To find the volume and surface area of the solid, we need to consider the cylinder and the two hemispheres separately.

1. Volume of the cylinder = πr²h

= 3.142 × (3.5 cm)² × 5.25 cm

= 60.49 cm³

2. Surface area of the cylinder = 2πrh + 2πr²

= 2 × 3.142 × 3.5 cm × 5.25 cm + 2 × 3.142 × (3.5 cm)²

= 116.94 cm²

3. Volume of each hemisphere

= (2/3)πr³ = (2/3) × 3.142 × (3.5 cm)³

= 56.26 cm³

4. Surface area of each hemisphere = 2πr²

= 2 × 3.142 × (3.5 cm)²

= 77.33 cm²

5. Total volume of the solid = Volume of the cylinder + 2 × Volume of each hemisphere

= 60.49 cm³ + 2 × 56.26 cm³ = 172.01 cm³

6. Total surface area of the solid = Surface area of the cylinder + 2 × Surface area of each hemisphere

= 116.94 cm² + 2 × 77.33 cm²

= 271.60 cm²

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