Question

Answer please as best as u can it will help a lot thanks

Answer 1

Look at the picture.

The triangles ABC and DEC are similar. Therefore the sides are in proportion:

$\dfrac{AC}{DC}=\dfrac{AB}{DE}$

AC = 4cm + 16cm = 20cm

DC = 16cm

AB = 15cm

DE = r

Substitute:

$\dfrac{20}{16}=\dfrac{15}{r}\to\dfrac{5}{4}=\dfrac{15}{r}$      cross multiply

$5r=(4)(15)$

$5r=60$     divide both sides by 5

$r=12\ cm$

The volume of a larger cone:

$V_l=\dfrac{1}{3}\pi\cdot15^2\cdot20=\dfrac{1}{\not3_1}\pi\cdot15\!\!\!\!\diagup^5\cdot15\cdot20=1500\pi\ cm^3$

The volume of a smaller cone:

$V_s=\dfrac{1}{3}\pi\cdot12^2\cdot16=\dfrac{1}{\not3_1}\pi\cdot12\!\!\!\!\!\diagup^4\cdot12\cdot16=768\pi\ cm^3$

The volume of the frustum:

$V=V_l-V_s\to V=1500\pi-768\pi732\pi\ cm^3$

Answer: 732π cm³.