If the volume of tea in a tea bag is approx. 23cm^3, calculate the depth, d, of tea leaves in the bag. Round your final answer to 1 decimal place.

Question

The slant height of the pyramid = 7.7cm

The side of the base of the pyramid = 3.5cm

The perpendicular height of the pyramid = 7.291cm

The Base area = 12.25cm^2

 

FULL WORKING PLEASE!!!

Answer 1

The volume of a regular pyramid with base area B and perpendicular height h is:

(1/3)(B)(h)

The total volume of the bag is:

(1/3)(12.25)(7.291) =29.772 cm^3

Because the volume of tea is less than this, the empty space is:

29.772 - 23 = 6.772 cm^3 rounded to 6.77.

We can find the height (h2) of the empty area and then subtract from the total height to find the height of the tea.

The area of the base is proportional to the height.

Base of empty area is (12.25)(h2/7.291)=1.68h2

Volume of empty area is:
(1/3)(1.68h2)(h2)=.56h2^2=6.77
h2^2 =12.09
h2=3.48
The height of the tea is h –h2 = 7.291-3.48 = 3.81 =3.8 cm

Carl