Question

A closed cylindrical tank, made of thin ironsheet, has diameter = 8.4 m and height 5.4 m. How much metal sheet, to the nearest m², is used in making this tank, if `1/15` of the sheet actually used was wasted in making the tank?

Answer 1

Given:

Diameter of cylinder = 8.4 m → Radius

`r = 8.4/2`

= 4.2 m

Height = 5.4 m

Tank is closed, so surface area = CSA + Top + Bottom

Step 1: Calculate the Total Surface Area of the Closed Cylinder

2πrh = 2 × π × 4.2 × 5.4

= 2 × 3.14 × 4.2 × 5.4

= 142.1 m²

Area of two bases:

2πr² = 2 × 3.14 × (4.2)²

= 6.28 × 17.64

= 110.8 m²

Total Surface Area (without waste):

142.1 + 110.8

= 252.9 m²

Step 2: Let total metal sheet used = X

`(14X)/15`

= 252.9

X = 252.9 `xx 15/14`

X = 271.9 m²

= 272 m²