A solid cylinder has a total surface area of 462 sq.cm . If its curved surface area is one-third of its total surface area, then the volume of the cyl - Mathematics and Science MCQ UPTET Paper 2 (Maths & Science) 2026 | ExamTest.live

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A solid cylinder has a total surface area of 462 sq.cm . If its curved surface area is one-third of its total surface area, then the volume of the cylinder will be

Solution & Step-by-step Explanation

Given Total Surface Area (TSA) = 462 cm^{2} .Curved Surface Area (CSA) = \frac{1}{3} \times TSA = \frac{1}{3} \times 462 = 154 cm^{2} .We know: TSA = CSA + 2 π r^{2} 462 = 154 + 2 π r^{2} 2 π r^{2} = 462 - 154 = 308 2 \times \frac{22}{7} \times r^{2} = 308 \frac{44}{7} r^{2} = 308 ⟹ r^{2} = \frac{308 \times 7}{44} = 7 \times 7 = 49 r = 7 cm Now, use the CSA formula to find height (h): CSA = 2 π r h = 154 2 \times \frac{22}{7} \times 7 \times h = 154 44 h = 154 ⟹ h = \frac{154}{44} = 3.5 cm = \frac{7}{2} cm Calculate the volume (V): V = π r^{2} h = \frac{22}{7} \times 49 \times \frac{7}{2} = 11 \times 49 = 539 cm^{3}

Try it yourself before checking the explanation above.

A solid cylinder has a total surface area of 462 sq.cm . If its curved surface area is one-third of its total surface area, then the volume of the cylinder will be

639 cm^{3}

539 cm^{3}

439 cm^{3}

600 cm^{3}

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