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.

Step-by-step 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 = $\dfrac13\pi r^2 h$

Volume of lid  $=\dfrac13(3.14)(2.5)^2(4.5)=29.4375\approx29.44\text{ cm}^3$

Surface area of cone = $\pi r\sqrt{h^2+r^2}$  [as lide has no base we don't include area of base.]

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

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