Question

2. The volume of a right circular cylinder is 448 cm² and height 7 cm. Find the
lateral surface area and total surface area.​

Answer 1

Given:

The volume of a right circular cylinder is 448 cm³

The height of the right is 7 cm

To find:

• The Lateral Surface Area [i.e. Curved Surface Area(CSA) ] of the cylinder
• The Total Surface Area (TSA) of the cylinder

The formula used to find the Curved Surface Area(CSA) is

= 2πrh unit sq.

And

The formula of finding the Total Surface Area (TSA) of the cylinder is

= 2πr(r+h) units sq.

Now,

We can get the value of the radius (r) by using the formula of volume = πr²h unit cube.

⇒ 22/7 * (r)² * 7 = 448

⇒ 22 * r² = 448

⇒ r² = 448 ÷ 22

⇒ r² = 20.36

⇒ r = square root of (20.36)

⇒ r = 4.51 cm

Now,

• The Curved Surface Area of the cylinder is

= 2πrh unit sq.

= 2 * 22/7 * 4.51 * 7

= 2 * 22 * 4.51

= 198.44 cm sq.

• The Total Surface Area of the cylinder is

= 2πr(r+h) units sq.

= 2 * 22/7 * 4.51 * (4.51 + 7)

= 198.44/7 * (11.51)

= 2284.04/7

= 326.29 cm sq.

Hence,

Lateral Surface Area = 198.44 cm sq.

And

Total Surface Area = 326.29 cm sq.

Answer 2

Given:

• Volume of the cylinder is 448 cm³,
• height of the cylinder is 7 cm.

━━━━━━━━━━━━━━━━

Let the radius be r cm.

Volume of cylinder = πr²h

=> 448 = πr²h

=>$\dfrac{448×7}{22}= r² × 7$

=> 448 = r² × 22

=> $\dfrac{448}{22}=r²$

=> 20.36= r²

=> $\sqrt{20.3636}=r$

=> $\bold{\red{4.51cm= r}}$

━━━━━━━━━━━━━━━━

Thus,

The radius of the cylinder is 4.51 cm.

Need to Find:

Lateral surface area and total surface area of the cylinder.

Lateral Surface Area:

= 2πrh

= $2 ×\dfrac{22}{7}×7×4.51$

$\bold{\red{=198.44cm²}}$

━━━━━━━━━━━━━━━━

Total surface area:

= 2πr(r + h)

= $2 × \dfrac{22}{7}× 4.51×(4.51+ 7)$

=$\bold{\red{326.29cm²}}$