Question

6. What is the height of a cylindrical box of radius 10 cm and total surface area 942 cm2 ?​

Answer 1

Step-by-step explanation:

Radius of cylindrical box = 10 cm

Total Surface Area of cylindrical box = 942 cm²

To Find :-

• Height of the cylindrical box

Assumption:-

Let the height of the cylindrical box = h

Formula:-

T.S.A = 2πr (r + h)

Solution:-

As we know T.S.A = 942 cm²

So,

942 = 2πr (r + h)

Radius = 10 cm

⟹ 942 = 2 × 22/7 × 10 (10 + h)

⟹ 942 = 440/7 (10 + h)

⟹ 942 × 7 = 440 (10 + h)

⟹ 6594 = 440 (10 + h)

⟹ 6594/440 = (10 + h)

⟹ 3297/220 = (10 + h)

⟹ 3297/220 - 10/1 = h

⟹ 3297 - 2200/220 = h

⟹ 1097 / 220 = h

Height = 1097 / 220 cm

Verification:-

T.S.A = 2 × 22/7 × 10 (10 + 1097 / 220)

⟹ 942 = 440 / 7 ( 2200 + 1097 / 220)

⟹ 942 = 440 / 7 × 3097 / 220

⟹ 942 = 2 × 471

⟹ 942 = 942

\therefore∴ L.H.S = R.H.S

✒ Required Answer :-

Height of the cylindrical box = 1097 / 220 cm