Question

The volume of a right circular cone is 5 liters. Calculate the volumes of the two parts into which the cone is divided by a plane parallel to the base, one third of the way down from the vertex to the base. give your answer to the nearest ml.

Answer 1

Answer:

Then, since the two cones are similar, the volume of the small cone is (1/3)^3 = 1/27 the volume of the original cone. So the volumes of the two pieces are 1/27 of 5000 ml and 26/27 of 5000 ml.

Answer 2

Answer:

solution:

volume of the right circular cone

$\sf = \frac{1}{3} \times \pi {r}^{2} \times h = 5 \\ \\ \sf = \pi \times {r}^{2} \times h =5 \times 3 \\ \\ \sf \: = \pi \times {r}^{2} \times h = 15$

from the third part of the statement,

• the radius(r)=1/3r
• the height(h)=1/3h

The volume of the cone

$\sf = \frac{1}{3} \times \pi \times { \frac{1}{3r} }^{2} \times \frac{1}{3h} \\ \\ \\ \sf = \frac{1}{3} \pi \times { \frac{1}{9r} }^{2} \times \frac{1}{3} h \\ \\ \\ \sf = \frac{1}{3} \times \frac{1}{9} \times \frac{1}{3} \times \pi \times {r}^{2} \times h$

From equation one above

$\sf \: \pi \times {r}^{2} \times h = 15 \\ \\ \\ \sf= \frac{1}{81} \times 15 \\ \\ \\ \sf \leadsto0.185 \: ml \\ \\ \sf \leadsto185 \: ml$

I hope it helps u!!