Question

HELP 60 MIN LEFT A bottling company makes decorative bottles and ships them to their customers. Each bottle has a height of 13 inches and a radius of 2.5 inches. The manufacturer places each bottle in cylinder packaging and adds cushioning to the insides of the cylinder. The cushioning is an inch thick on each side of the bottle. If the height of the cylinder is the same as the height of the bottle, what is the volume of the cylinder used to package the bottles? (Round to the nearest whole number. Use π=3.14.) A 102in3 B 255in3 C 500in3 D 2000in3

Answer 1

The volume of the cylinder used to package the bottles is 500$in^3$.

Option: C.

Step-by-step explanation:

Bottles are decorated with using cylinder package and cushions with it.

The height of the bottle is 13 inches.

The radius of the bottle is 2.5 inches.

The thickness of the cushion is 1 inch.

The volume of the cylinder = π$r^2 h$.

The height of the bottle is same as the height of the cylinder. Then the height of the cylinder is 13 inches.

The cylinder comprises of both cushion and bottle. Then the diameter or radius of the cylinder is sum of the thickness of the cushion with the bottle's diameter or radius.

∴radius of the cyinder = radius of bottle +thivhess of cushion.

= 2.5+1.

=3.5 inches.

The volume of the cylinder = 3.14×3.5×3.5×13.

=500.3 $in^3$ ≈ 500

Thus the volume = 500 $in^3$.