Question

(i) Draw a cone and its net
(ii) A sphere of radius is equal to ${{\dfrac{1}{3}}^{rd}}$ of the height of the cylinder is kept in the equal cylinder of equal cylinder. Draw its 3D figure.

Answer 1

Hint: In (i) part we have to draw a cone and its net. A net is a 2D shape that is folded to form a 3D shape. So we will first draw a cone and then find the two shapes which make a cone. For (ii) part, we will suppose the height of the cylinder as h and then make a sphere with ${{\dfrac{1}{3}}^{rd}}$ of h enclosed inside the cylinder.

Complete step by step answer:
(i) Let us first understand the meaning of a net of a solid. A net is a 2 dimensional shape that can be folded to form a 3 dimensional shape or solid. It is a pattern made when the surface of a three dimensional figure is laid out flat showing each face of a figure. Number of shapes in the net is equal to the number of faces of the shape.
For a cone, we know it has two faces, so its net will have two shapes. One shape will be a circle which is the base of the cone. Another shape is the cut out circle i.e. when a segment is cut out a circle.
A cone with radius r and slant height l looks like this,

Its net will look like this,

Hence we have obtained the required figure of net.
(ii) We need to make a three dimensional figure of a sphere enclosed in a cylinder. The radius of the sphere is ${{\dfrac{1}{3}}^{rd}}$ of the height of the cylinder. The radius of the base of the cylinder is equal to the radius of the cylinder. Let us suppose that h is the height of the cylinder. Therefore, the radius of the sphere will be ${{\dfrac{1}{3}}^{rd}}$ of h i.e. $\dfrac{1}{3}h$. Similarly, the radius of the base of the cylinder will be $\dfrac{1}{3}h$.
Our figure looks like this,

Note: Students should carefully label the diagram with proper variables. In the net of the cone we can also use the measurement of height h but it is not necessary. Try to make diagrams using proper scale. Make sure that the net of any solid has an equal number of shapes as that of the number of faces of the solid.