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Work out the surface area of this cylinder.

12 cm radius
35 cm height


Sagot :

Answer:

The surface area of this cylinder is 3545[tex]\frac{1}{7}[/tex] cm²

Step-by-step explanation:

The formula of the surface area of the cylinder is

  • Surface area = later area + 2 base area, where
  • Lateral area = perimeter of the base × height of the cylinder

Let us use the rules above to solve the question

∵ The base of the cylinder is a circle

∵ The perimeter of the circle = 2 π r

∵ The radius of the cylinder is 12 cm

r = 12

∴ The perimeter of the base = 2 (12) (π)

The perimeter of the base = 24π cm

∵ The height of the cylinder is 35 cm

h = 35 cm

→ By using the rule of the lateral area above

∵ The lateral area = 24π × 35

∵ π = [tex]\frac{22}{7}[/tex]

∴ The lateral area = 24 × [tex]\frac{22}{7}[/tex] × 35

The lateral area = 2640 cm²

∵ The area of the circle = π r²

∴ The area of the base = [tex]\frac{22}{7}[/tex] × (12)² = [tex]\frac{22}{7}[/tex] (144) = 452[tex]\frac{4}{7}[/tex] cm²

→ By using the rule of the surface area above

∴ The surface area = 2640 + 2(452[tex]\frac{4}{7}[/tex]) = 3545[tex]\frac{1}{7}[/tex] cm²

The surface area of this cylinder is 3545[tex]\frac{1}{7}[/tex] cm²