The diameter of a cylinder is 28 cm and its height is 20 cm. Find its total surface area.​

2 thoughts on “The diameter of a cylinder is 28 cm and its height is 20 cm. Find its total surface area.​”

1. Given:

   A cylinder with –

   • Diameter = 28 cm
   • Height = 20 cm

   What To Find:

   We have to find –

   • The total surface area.

   Formula Needed:

   [tex]\bf \mapsto TSA = 2 \pi r^2 + 2 \pi rh[/tex]

   Where –

   • TSA = Total surface area.
   • R = radius
   • H = Height

   Solution:

   • Finding the radius.

   We know that –

   [tex]\sf \mapsto R = \dfrac{Diameter}{2}[/tex]

   Substitute the value,

   [tex]\sf \mapsto R = \dfrac{28}{2}[/tex]

   Divide 28 by 2,

   [tex]\sf \mapsto R = 14 \: cm[/tex]

   • Finding the TSA.

   Using the formula,

   [tex]\sf \mapsto TSA = 2 \pi r^2 + 2 \pi rh[/tex]

   Substitute the values,

   [tex]\sf \mapsto TSA = 2 \times \dfrac{22}{7} \times 14 \times 14 + 2 \times \dfrac{22}{7} \times 14 \times 20[/tex]

   Multiply 14 with 14,

   [tex]\sf \mapsto TSA = 2 \times \dfrac{22}{7} \times 196 + 2 \times \dfrac{22}{7} \times 14 \times 20[/tex]

   Multiply 14 with 20,

   [tex]\sf \mapsto TSA = 2 \times \dfrac{22}{7} \times 196 + 2 \times \dfrac{22}{7} \times 280[/tex]

   Cancel 7 and 196,

   [tex]\sf \mapsto TSA = 2 \times 22 \times 28 + 2 \times \dfrac{22}{7} \times 280[/tex]

   Cancel 7 and 280,

   [tex]\sf \mapsto TSA = 2 \times 22 \times 28 + 2 \times 22 \times 40[/tex]

   Multiply 2, 22, and 28,

   [tex]\sf \mapsto TSA = 1232 + 2 \times 22 \times 40[/tex]

   Multiply 2, 22, and 40,

   [tex]\sf \mapsto TSA = 1232 + 1760[/tex]

   Add 1232 and 1760,

   [tex]\sf \mapsto TSA = 2992 \: cm^2[/tex]

   Final Answer:

   ∴ Thus, the total surface area of the cylinder is 2992 cm².

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2. Answer:

   2992 cm = 29.92 m

   Step-by-step explanation:

   Radius = Diameter / 2 = 28/2 = 14cm

   [tex]tsa \: of \: a \: cylinder = 2\pi \times r(r + h)[/tex]

   =>tsa = (2 x 22 x 14)(14 + 20)/7 = 2992 cm

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