Question

The tsa of a solid cylinder is 462 cm square and its csa is one third of tsa. Find volume of the cylinder

Answer 1

answer 539
hope it helps

Answer 2

$<b>Answer</b>$ : 538 cm³

$<b>Step-by-step explanation</b>$ :

Total Surface Area of cylinder

= 2πr( h + r ) or 2πrh + 2πr²

$<b>Curved Surface Area = ⅓ Total Surface Area</b>$

2πrh = ⅓ × 462 cm²

2πrh = 154 cm²

Since 2πrh + 2πr² = 462 cm²

154 cm² + 2πr² = 462 cm²

2πr² = 462 - 154 cm²

2πr² = 308 cm²

$<b>r² = 308/2π</b>$

r² = 308 × 1/2 × 7/22 cm²

r² = 28 × 1/2 × 7/2 cm²

r = √49 cm² = 7 cm

$<b>Therefore, 2πrh = 154 cm²</b>$

h = 154/2 × 1/(πr)

h = 154 × 1/2 × 7/22 × 1/7 cm

$\bf{\boxed{\boxed{h \:\:= 3.5\: cm}}}$

Volume of cylinder = πr²h

Volume of cylinder = 22/7 × 7² × 3.5 cm³

$<b>Volume of cylinder = 539 cm³</b>$