Question

A tin of Tonyz soup has a paper label wrapped around the outside. The tin has a height of 21cm and a radius of 7cm. The label covers the entire height of the can. The label overlaps by 1cm as it wraps around so that it can be stuck together. Calculate the area of the label. 7cm Tonyz Cream of EST 1986 EST Tomato Soup VRISTES 14.1 OZ (40g) 12 21cm​

Answer 1

944.6 cm²

Explanation:

You want the area of a label that covers the lateral surface of a cylinder with a 1 cm overlap of the ends. The cylinder is 7 cm in radius and 21 cm high.

Circumference

The circumference of the cylinder is ...

C = 2πr

C = 2π(7 cm) = 14π cm ≈ 43.982 cm

Area

The area of the label is the product of its length and width. The length is 1 cm more than the circumference, so the area is ...

A = LW = (43.982 +1 cm)(21 cm) ≈ 944.6 cm²

The area of the label is about 944.6 cm².