Question

a rocket in the shape of a cone is attached to a cylinder with the same base radius. the cone has a slant height of 15m. the cylinder has a base diameter of 12m and a height of 42m.find the total surface area of the rocket.

Answer 1

Answer:

The total surface area of the rocket = 1980 m²

Step-by-step explanation:

Given:

• Slant height of a cone = 15 m
• Radius of a cone = 6 m
• Radius of a cylinder = 6 m
• Height of a cylinder = 42 m

To find:

• The total surface area of the rocket.

Solution:

✰ Curved surface area of cone = πrl

Where,

r is the radius of a cone.

l is the slant height of a cone.

Putting the values in the formula, we have:

• Curved surface area of cone = 22/7 × 6 × 15
• Curved surface area of cone = 22/7 × 90
• Curved surface area of cone = 1980/7
• Curved surface area of cone = 282.86 m²

✰ Curved surface area of cylinder = 2πrh

Where,

r is the radius of a cylinder.

h is the height of a cylinder.

Putting the values in the formula, we have:

• Curved surface area of cylinder = 2 × 22/7 × 6 × 42
• Curved surface area of cylinder = 2 × 22 × 6 × 6
• Curved surface area of cylinder = 44 × 36
• Curved surface area of cylinder = 1584 m²

✰ Area of a base of a cylinder = πr²

Where,

r is the radius of a cylinder.

Putting the values in the formula, we have:

• Area of a base of a cylinder = 22/7 × 6 × 6
• Area of a base of a cylinder = 22/7 × 36
• Area of a base of a cylinder = 792/7
• Area of a base of a cylinder = 113.14 m²

Finally,

• The total surface area of the rocket = Curved surface area of cone + Curved surface area of cylinder + Area of a base of a cylinder

• The total surface area of the rocket = 282.86 + 1584 + 113.14

• The total surface area of the rocket = 282.86 + 1697.14

• The total surface area of the rocket = 1980 m²

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