Question

The spherical bottle has a conical shaped lid with a diameter of 5cm and a height of 4.5cm. Given this information, calculate the volume and surface area of the lid of the spherical shaped bottle.

Answer 1

Answer: Volume of lid = 29.44 cubic cm and surface area = 40.41 cubic cm.

Explanation:

Given: For lid of the spherical shaped bottle,

Diameter = 5 cm

Height = 4.5 cm

Radius = Half of diameter = 2.5 cm

Volume of cone =
`\frac13\pi r^2 h`

Volume of lid
`=\frac13(3.14)(2.5)^2(4.5)=29.4375\approx29.44\text{ cm}^3`

Surface area of cone =
`\pi r√(h^2+r^2)` [as lide has no base we don't include area of base.]

Surface area of lid =
`(3.14)(2.5)√((2.5)^2+(4.5)^2)= 7.85√(26.5)\approx40.41\text{ cm}^3`

Hence, volume of lid = 29.44 cubic cm and surface area = 40.41 cubic cm.