Question

A cone of base radius 4 cm is divided into two parts by drawing a plan
the mid-point of its height and parallel to its base. Compare the volume of
two parts.​

Answer 1

Answer:

i think it is frustum bcz after dividing cone it is called frustum apply volume of frustum

Step-by-step explanation:

1/3 πh(R²+r²+Rr,)

Answer 2

The volumes of the two parts is 1:7.

Step-by-step explanation:

Radius of the cone (r) = 4 cm

Let us consider h be the height of the original cone

Its divided into two parts by drawing plane mid point through its axis and parallel to its base.

∴ A new small cone ADE is formed at the top and a Frustum DECG is formed.

$\text{Height of small cone} = \frac{h}{2} \ \text{cm}$

In ΔAFE and ΔABC,

∠AFE = ∠ABC = 90°

∠FAE = BAC ( common angle)

DE║GC

∴∠AEF =∠ACB ( Corresponding Angles)

Hence ΔAFE≈ΔABC

∴The ratio of their corresponding sides are also equal,

$\frac{\frac{\text{h}}{2} }{\text{h}} = \frac{\text{FE}}{\text{BC}}$

$\frac{1}{2} = \frac{\text{FE}}{4}$

∴ FE = 2 cm

$\text {The volume of the cone} = \frac{1}{3} \pi \text{r}^2\text{h} \ \ \text{Cubic units}$

$\text {The volume of the cone AGC} = \frac{1}{3} \pi {4}^2\text{h} \ \ \text{Cubic units}$  

$\text {The volume of the cone AGC} = \frac{16}{3} \pi \text{h} \ \ \text{cm}^3$

$\text{The volume of the cone ADE} = \frac{1}{3} \pi {2}^2\text{h} \ \ \text{cm}^3$

$\text{The volume of the cone ADE} = \frac{1}{3} \times 4\pi \frac{\text{h}}{2} \ \ \text{cm}^3$

$\text{The volume of the cone ADE} = \frac{2}{3} \pi \text{h}\ \ \text{cm}^3$                             

Volume of Frustum DGCE = Volume of AGC - Volume of cone ADE

$\text{The volume of Frustum DGCE} =\frac{16}{3} \pi \text{h} - \frac{2}{3} \pi \text{h}\ \ \text{cm}^3$

$\text{The volume of Frustum DGCE} =\frac{14}{3} \pi \text{h} \ \text{cm}^3$                    

The ratio of two parts = Volume of cone ADE : Volume of Frustum DGCE

$\text{The ratio of two parts} =\frac{2}{3} \pi \text{h}\ : \frac{14}{3} \pi \text{h}$

The ratio of the two parts = 1 : 7

To Learn More.....

1. From a solid wooden sphere with 13 centimetres radius, a cone with 18 centimetres height and maximum base is made.

[31 (a) Taking the base radius of the cone as r draw a rough figure.

(b) Calculate the radius of the cone. (c) What is the volume of the cone?​

brainly.in/question/14457250

2. Find the slant height and radius of the cone made from a quadrant of a circle of radius 9.6cm

brainly.in/question/955520