Question

the total surface area of a solid cylinder is 462 CM square and its curved surface area is one third of its total surface area find the volume of the cylinder

Answer 1

TSA of cylinder = 462 cm^2
according to the question
TSA=CSA+2×PIE ×R^2
TSA=1/3×TSA+2×PIE×R^2
TSA -TSA /3= 2×PIE×R^2
2TSA /3 =2×PIE×R^2
2×462/3=2×PIE×R^2
308=2×22/7×R^2
308×7/2×22=R^2
196=R^2
14=R
TSA =2×PIE×R(R+H)
462=2×22/7×14 (14+H)
462=2×22×2 (14+H)
462/2×22×2=(14+H)
5.25=14+H
8.75=h
volume of cylinder =pie×r^2×h
=22/7×14×14×8.75=5390

Answer 2

$\huge{\mathfrak{\red{Answer}}}$

Curved surface area = total surface area / 3.

Curved surface area = 462/3 = 154.

Rest of area = 462 - 154 = 308.

$\longrightarrow$2πr^2 = 308.

$\longrightarrow$r^2 = 308 x 7 / 44 = 49.

$\longrightarrow$r = 7.

2πrh = 154.

h = 154 / 2 x 22 = 7/2.

$\longrightarrow$Volume = πr^2 h = (22/7) x (7^2) x (7/2) = 539.

$\rm Volume = 539 cm^3$