Question

a solid cylinder has T.S. A of 462, sq.cm .Its curved surface area is 1/2 find the volume of
cylinder- (π=22/7)
​

Answer 1

Answer:

By Yoshana Chaudhary

Step-by-step explanation:

The surface area has to be 1/3rd.

SOLUTION

Curved surface area = total surface area / 3.

Curved surface area = 462/3 = 154.

Rest of area = 462 - 154 = 308.

2πr^2 = 308.

r^2 = 308 x 7 / 44 = 49.

r = 7.

2πrh = 154.

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

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

Volume = 539 cm^3

Answer 2

$\bf\large{\underline{qUESTIOn:-}}$

a solid cylinder has T.S.A of 462, sq.cm .Its curved surface area is 1/2 find the volume of

cylinder- (π=22/7)

$\bf\large{\underline{gIVEn:-}}$

• T.S.A of cylinder = 462 sq.cm
• Curved surface area = 1/2

$\bf\large{\underline{To Find:-}}$

• Volume of cylinder =?

$\bf\large{\underline{sOLUTIOn:-}}$

• T.S.A= 462sq.cm
• C.S.A =1/3 of total surface area.

$\bf\large{\underline{aCOORDINg\:To\: qUESTIOn:-}}$

$\tt→\frac{c.s.a}{t.s.a}=\frac{1}{3}\\\tt→ \frac{2πrh}{2πr(r+h)}=\frac{1}{3}\\\tt→ \frac{h}{r+h}=\frac{1}{3} (on\: reversing)\\\tt→ \frac{r+h}{h}=\frac{3}{1}\\\tt→ \frac{r}{h}+\frac{h}{h}=\frac{3}{1}\\\tt→ \frac{r}{h}=\frac{3-1}{1}\\\tt→\frac{r}{h}=\frac{2}{1}\\\tt→ 2h=r$

★ Now,

• Total surface area = 2πr(r+h)

t.s.a is given = 462cm sq.unit

$\tt→462=2πr^2+2πrh\\\tt→462=2πr^2+154\\\tt→2πr^2=462-154\\\tt→ 2πr^2=308\\\tt→ r^2=\frac{308×6}{2×22}\\\tt→ r^2=\frac{308}{44}\\\tt→ r=\sqrt49\\\tt→ r=7$

◇ Therefore,

$\tt→2h=r\\\tt→ 2h=7\\\tt→ h=\frac{7}{2}\\\tt→h=3.2cm$

◆Now,

$\tt Volume(v)=πr^2h\\\tt→ V=\frac{22}{7}×7×7×3.5\\\tt→ V = 11×7×7\\\tt→ V= 11×49\\\tt→ 539cm^3$

Hence,

Volume of the cylinder is$\tt= 539cm^3$