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The height of the two prisms is 14 cm and 10 cm. The ratio of the area of bases of two square prisms is 7 ∶ 9 and the volume of the first prism is 882 cm3 then what is the total surface area of the second prism?1. 522 cm22. 542 cm23. 512 cm24. 532 cm2 |
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Answer» Correct Answer - Option 1 : 522 cm2 Given: The heights of the two prisms are 14 cm and 10 cm The ratio of the area of bases of two square prisms are 7 ∶ 9 The volume of first prism = 882 cm3 Formula used: The volume of the square prism = Area of the base × height The total surface area of the square prism = 2 × Area of base + 4 × Area of lateral sides Calculation: Let the area of the base of the first and second prism be 7x and 9x The volume of the first prism = Area of the base × height ⇒ 7x × 14 = 882 ⇒ x = 9 So, Area of the base of the second prism = 9 × 9 = 81 So, The length of the side of the second prism = √81 = 9 cm Now, Total surface area of the second prism = 2 × area of base + 4 × area of the lateral side ⇒ 2 × 92 + 4 × 9 × 10 = 522 cm2 ∴ The Total surface area of the second square prism is 522 cm2 |
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