Question

Two similar solid cones have their radii 15cm and 25cm respectively, if the volume of the bigger cone is 325cm³. Calculate (a) the linear scale factor (b) the volume scale factor (c) volume of the smaller cone​

Answer 1

a) the linear scale factor = 5/3

b) the volume scale factor = 125/27

c) 70.2 cm³

Explanation:

r₁ = 15 cm, r₂ = 25 cm

r₂/r₁ = 25/15 = 5/3

They are similar, so h₂/h₁ = 5/3

a) the linear scale factor = 5/3

b) the volume scale factor = (5/3)³ = 125/27

c) V₂/V₁ = 125/27

Given V₂ = 325 cm³, V₁ = 325*27/125 = 70.2 cm³

Answer 2

The length scale factor = \(\frac{24}{6} = 4\)

The area scale factor = \(4^2 = 16\)

\[\text{Larger area} = 16 \times \text{smaller area}\]

\[50.3 \times 16 = 804.8\]

The area of the large clock face is approximately 804.8 cm2.

Explanation:

The length scale factor = \(\frac{24}{6} = 4\)

The area scale factor = \(4^2 = 16\)

\[\text{Larger area} = 16 \times \text{smaller area}\]

\[50.3 \times 16 = 804.8\]

The area of the large clock face is approximately 804.8 cm2.