Thevolume of a right circular cone is 5 litres.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.

Question

Thevolume of a right circular cone is 5 litres.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.

Answer 1

Please can you throw more light to this question and the solution you gave above. Thanks

Answer 2

Please could you throw more light to the solution. Thanks

Answer 3

Please can you throw more light to this question and it solution

Answer 4

Use linear ratio

5000ml-5000ml(1/27)
5000ml-185ml
=4815ml

Answer 5

To 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, we need to divide the given cone in a specific ratio.

Let's solve this step by step:

Step 1: Determine the volume of the entire cone
Given that the volume of the entire cone is 5 litres, let's denote it as V.

Step 2: Calculate the ratio of the two parts
The plane that divides the cone is parallel to the base and located one-third of the way down from the vertex to the base. This means that the ratio of the volumes between the smaller cone and the larger cone is 1:2.

Step 3: Find the volume of the larger cone
The larger cone constitutes 2 parts out of the total 3 parts. Therefore, the volume of the larger cone is (2/3) * V.

Step 4: Find the volume of the smaller cone
The smaller cone constitutes 1 part out of the total 3 parts. Therefore, the volume of the smaller cone is (1/3) * V.

Step 5: Conversion to Litres
Since the question specifies the volume of the cone as 5 liters, let's convert the calculated volumes to litres.

Now, let's substitute V = 5 litres into the formulas:

Volume of the larger cone = (2/3) * 5 = 10/3 litres
Volume of the smaller cone = (1/3) * 5 = 5/3 litres

Hence, the volume of the larger cone is (10/3) litres, and the volume of the smaller cone is (5/3) litres.

Answer 6

I solved this problem but no access here to upload pictures,i wud hav uploaded the comprehensive solution

Answer 7

since volume scales as the cube of the linear ratio, the small cone has 1/27 the volume of the whole cone.

So, the parts' volumes are 5(1/27) and 5(26/27)