$(a)$ Renewable Energy:A renewable source of energy is defined as the sources of energy that are being produced continuously means they are inexhaustible in nature and can be used for a very long period of time are called renewable sources of energy.Examples: Wind Energy, Solar Energy, Hydro Energy, and Biomass. Non-renewable Energy:They are non-renewable because they are present in limited amounts in nature, and once exhausted, cannot be replenished or regained.Non- Renewable sources of energy - Coal, Petroleum, Natural gas. Renewable sources of energy - Wind, Tides, Wood.The difference between a renewable and a non-renewable source of energy are:Renewable Source of EnergyNon-Renewable Source of Energy1. It can be used again and again ... Read More

A source of energy is defined as the source which can provide an adequate amount of energy in a convenient form for a long period of time.The two main categories of sources of energy are:(i) Renewable source of energy.       (ii) Non-renewable source of energy.On the basis of availability, natural resources are divided into two types:1. Renewable- These types of resources are available in infinite quantity and can be replenished naturally and used repeatedly. Example- Sunlight, wind, water, etc.2. Non-Renewable- These types of resources are limited because either they form slowly, or do not form naturally in the environment due to their non-renewable nature. Their availability may run ... Read More

The advantages of solar cells are as follows:1. They do not have moving parts and require no maintenance.2. They can be used even in remote and inaccessible areas.3. It saves fossil fuels like coal, kerosene, petroleum, etc, which are non-renewable.4. It does not produce any harmful smoke and ash that pollutes the air.5. It does not spoil the nutrients present in the food.The disadvantages of solar cells are as follows:1. They are very expensive, as they require a special grade of silicon or silver wire.2. They are less efficient, as they can convert only about 25% of the light falling on ... Read More

The environmental consequences of the increasing demand for energy are as follows:1. Setting up more nuclear power plants increases the radioactivity in the environment.2. Construction of hydropower plants is disturbing the ecological balance.3. The combustion of fossil fuels causes acid rain, due to which plants, soil, and aquatic life get damaged.4. The combustion of fossil fuels also increases the greenhouse gasses (carbon dioxide) which pollute air present in the atmosphere.Steps for reducing energy consumption are given below:1. Switch off all the electrical devices such as TV, lights and fans when not needed.2. Energy-efficient electrical appliances should be used.3. Solar cookers and pressure cookers should be used for ... Read More

Given:An oil funnel made of tin sheet consists of a \( 10 \mathrm{~cm} \) long cylindrical portion attached to a frustum of a cone. The total height is \( 22 \mathrm{~cm} \), diameter of the cylindrical portion is \( 8 \mathrm{~cm} \) and the diameter of the top of the funnel is \( 18 \mathrm{~cm} \).To do:We have to find the area of the tin sheet required to make the funnel.Solution:Diameter of the upper circular end of frustum $= 18\ cm$This implies, Radius of the upper circular end of frustum $(r_1) = 9\ cm$The radius of the lower circular end ... Read More

To do:We have to derive the formula for the volume of the frustum of a cone.Solution:Let $ABC$ be a cone.From the cone the frustum $DECB$ is cut by a plane parallel to its base.$r_1$ and $r_2$ be the radii of the frustum ends of the cone and $h$ be the height of the frustum.In $\triangle ABG$ and $\triangle ADF$$DF \| BG$Therefore, $\triangle ABG \sim \triangle ADF$This implies, $\frac{D F}{B G}=\frac{A F}{A G}=\frac{A D}{A B}$$\frac{r_{2}}{r_{1}}=\frac{h_{1}-h}{h_{1}}=\frac{l_{1}-l}{l_{1}}$$\frac{r_{2}}{r_{1}}=1-\frac{h}{h_{1}}=1-\frac{l}{l_{1}}$$1-\frac{h}{\mathrm{h}_{1}}=\frac{r_{2}}{r_{1}}$$\frac{h}{\mathrm{h}_{1}}=1-\frac{r_{2}}{r_{1}}$$\frac{h}{\mathrm{h}_{1}}=\frac{r_1-r_{2}}{r_{1}}$$\frac{h_1}{h}=\frac{r_1}{r_1-r_2}$$h_1=\frac{r_1h}{r_1-r_2}$Volume of frustum of the cone $=$ Volume of cone $ABC -$ Volume of cone $ADE$$=\frac{1}{3}\pi r_1^2h_1 -\frac{1}{3}\pi r_2^2(h_1 - h)$$= \frac{\pi}{3}[r_1^2h_1-r_2^2(h_1 - h)]$$=\frac{\pi}{3}[r_{1}^{2}(\frac{h r_{1}}{r_{1}-r_{2}})-r_{2}^{2}(\frac{h r_{1}}{r_{1}-r_{2}}-h)]$$=\frac{\pi}{3}[(\frac{h r_{1}^{3}}{r_{1}-r_{2}})-r_{2}^{2}(\frac{h ... Read More

To do:We have to derive the formula for the curved surface area and total surface area of the frustum of the cone.Solution:Let $ABC$ be a cone. From the cone the frustum $DECB$ is cut by a plane parallel to its base.$r_1$ and $r_2$ be the radii of the frustum ends of the cone and $h$ be the height of the frustum.In $\triangle ABG$ and $\triangle ADF$$DF \| BG$Therefore, $\triangle ABG \sim \triangle ADF$This implies, $\frac{D F}{B G}=\frac{A F}{A G}=\frac{A D}{A B}$$\frac{r_{2}}{r_{1}}=\frac{h_{1}-h}{h_{1}}=\frac{l_{1}-l}{l_{1}}$$\frac{r_{2}}{r_{1}}=1-\frac{h}{h_{1}}=1-\frac{l}{l_{1}}$$1-\frac{l}{\mathrm{l}_{1}}=\frac{r_{2}}{r_{1}}$$\frac{l}{l_{1}}=1-\frac{r_{2}}{r_{1}}$$\frac{l}{l_{1}}=\frac{r_{1}-r_{2}}{r_{1}}$$\Rightarrow l_{1}=\frac{r_{1} l}{r_{1}-r_{2}}$..............(i)Curved surface area of frustum $D E C B=$ Curved surface area of cone $A B C$-Curved surface ... Read More

Given:In one fortnight of a given month, there was a rainfall of \( 10 \mathrm{~cm} \) in a river valley. The area of the valley is \( 7280 \mathrm{~km}^{2} \).To do:We have to show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each \( 1072 \mathrm{~km} \) long, \( 75 \mathrm{~m} \) wide and \( 3 \mathrm{~m} \) deep.Solution:Height of the rain $=10\ cm$$=\frac{10}{100}\ m$$=\frac{10}{100\times1000}\ km$Total rainfall in the river valley $=$ area of the valley $\times$ height of the rain$=7280\times\frac{10}{100\times1000}$$=0.7280\ km^3$Volume of normal water in each river $=1072\times\frac{75}{1000}\times\frac{3}{1000}$$= 0.2412\ km^3$Volume ... Read More

Given:A cistern, internally measuring \( 150 \mathrm{~cm} \times 120 \mathrm{~cm} \times 110 \mathrm{~cm} \), has \( 129600 \mathrm{~cm}^{3} \) of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water.Dimensions of each is \( 22.5 \mathrm{~cm} \times 7.5 \mathrm{~cm} \times 6.5 \mathrm{~cm} \).To do:We have to find the number of bricks that can be put in without overflowing the water.Solution:The dimensions of the cistern are \( 150 \mathrm{~cm} \times 120 \mathrm{~cm} \times 110 \mathrm{~cm} \)This implies, Volume of the cistern $= 1980000\ ... Read More

Given:A right triangle, whose sides are \( 3 \mathrm{~cm} \) and \( 4 \mathrm{~cm} \) (other than hypotenuse) is made to revolve about its hypotenuse. To do:We have to find the volume and surface area of the double cone so formed.Solution:Let $AB=3\ cm$ and $BC=4\ cm$ be the two sides of the right triangle $ABC$.This implies, using Pythagoras theorem, $AC^2=AB^2+BC^2$$AC^2=3^2+4^2$$=9+16$$=25$$\Rightarrow AC=\sqrt{25}$$=5\ cm$When the triangle $ABC$ is revolved about the hypotenuse $AC$, the following double cone is formed.In $\triangle \mathrm{ABC}$ and $\triangle \mathrm{BDC}$, $\angle \mathrm{ABC}=\angle \mathrm{CDB}=90^{\circ}$           ($\mathrm{BD} \perp \mathrm{AC})$)$\angle \mathrm{BCA}=\angle \mathrm{BCD}$           (Common)Therefore, by AA similarity, ... Read More