Question
Download Solution PDFIf the base of a prism is a square of side 8 cm. If the height of the prism is 20 cm, then, find the total surface area of the prism.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The base of a prism is a square of side 8 cm
The height of the prism is 20 cm
Formula used:
Total surface area of prism = Lateral surface area of prism + 2(Area of base)
Lateral surface area of prism = Perimeter of base × Height
Area of square = side × side
Calculations:
According to the question, we have
The side of base of a prism is a square of side 8 cm
So, The Area of square is
⇒ Area = Sides × Sides
⇒ Area = 8 × 8
⇒ Area = 64 cm2
And, Perimeter of square is
⇒ Perimeter = 4 × Sides
⇒ Perimeter = 4 × 8
⇒ Perimeter = 32 cm
The Lateral surface area of prism is
Lateral surface area of prism = Perimeter of base × Height
⇒ Lateral surface area of prism = 32 × 20
⇒ Lateral surface area of prism = 640 cm2
Now, The total surface area of a right square prism is
Total surface area of prism = Lateral surface area of prism + 2(Area of base)
⇒ Total surface area of prism = 640 + 2(64)
⇒ Total surface area of prism = 640 + 128
⇒ Total surface area of prism = 768 cm2
∴ The total surface area of the prism is 768 cm2.
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