Geometry integration? Need step by step help

Question

The bottom of the storage basket is a square with a side length of 20 cm. The edges tilt outwards by 2 cm whenever the height increases by 10 cm. What is the volume of the basket when the height of the basket is 30 cm

Answer 1

Basket is a trunk pyramid.

Volume of trunk pyramid=Volume of whole pyramid - Volume of top part that is a small pyramid

The base of the basket reflexes a square of 20cm each side.

Square area formula is A=a² that is A.base of the pyramid

For every 10 cm of height each side increases 2cm. So, at h=10cm the length of each side is 24.

For h=30cm each side will be 32cm. it is for the ratio of proportionality in similar triangles.

A. base of pyramid=32cmx32cm=1024cm²

The right triangle is formed by the height of 30 cm and the side formed by 20cm/2=10cm and the increased 6cm. So de total length of that side will be 10cm+6cm=16cm

Now it is proportion time with heights where x is the total height of the whole pyramid.

30cm/x=6cm/16cm

x=80cm

Total height is 80cm (ht)

Volumen of total pyramid= Abase x ht/3=32cmx32cmx80cm/3= 27306.6 cm³

h of top part of pyramid=ht-h=80cm-30cm=50cm

Volume top pyramid= Abase of top part x h top part

Volumen top pyramid= (20cm)² x 50cm/3= 6666.6cm³

Volume of trunk pyramid=Volumen total-Volume of top part

Volume of trunk pyramid= 27306.6cm³-6666.6cm³=20640cm³

The volume of the trunk pyramid is 20,640cm³

Answer 2

The bottom of the basket is 20 x 20

The top of the basket it 26 x 26

The height of the basket is 10

V = (1/3)[(20²) + (20)(26) + (26²)](10