A closed metallic cylindrical container is 1.05 m high and its base radius is 35 cm. If the metal sheet costs Rs 150 per m², then find the cost of the material used in this container. (Use π = \( \frac{22}{7} \))
To find the cost of the material used in the cylindrical container, we first need to calculate the total surface area of the closed cylinder. The total surface area of a closed cylinder is given by the formula \(2\pi r(h+r)\), where \(r\) is the radius of the base and \(h\) is the height. After calculating the area in square meters, we will multiply it by the cost per square meter to find the total cost.
B) Rs 462 is the correct cost of the material used in the container.
To find the ratio of the number of girls to the number of boys, we first need to calculate the number of girls. We are given the total number of students and the number of boys. Once we have the number of girls and boys, we can form the ratio and simplify it to its lowest terms.
The number of girls can be found by subtracting the number of boys from the total number of students.
\[ \text{Number of girls} = \text{Total students} - \text{Number of boys} \]\[ \text{Number of girls} = 162 - 72 \]\[ \text{Number of girls} = 90 \]The question asks for the ratio of the number of girls to the number of boys.
\[ \text{Ratio} = \text{Number of girls} : \text{Number of boys} \]\[ \text{Ratio} = 90 : 72 \]To simplify the ratio, find the greatest common divisor (GCD) of \(90\) and \(72\). Both numbers are divisible by \(18\).
So, the simplified ratio is \(5 : 4\).
Correct Option: B) 5 : 4
The question asks to identify which phenomenon is based on the principle of electromagnetic induction. We need to recall the definition of electromagnetic induction and then evaluate each option against this principle.
Correct Option: D) The relative motion between a coil and a bar magnet induces electric current.
To solve this problem, we first need to arrange the letters of the given word in alphabetical order. Then, we identify the letter that is third from the left and the letter that is fifth from the right in this new arrangement. Finally, we count the number of letters in the English alphabetical series that fall between these two identified letters.
C) One — As determined in the step-by-step analysis, there is only one letter (F) between E and G in the English alphabetical series.
Evaluate
\(\frac{(40.25\div5)+(0.07\times5)}{(0.15\times8)+(0.18\div0.2)}\)
To evaluate the given expression, we need to perform the operations in the correct order (BODMAS/PEMDAS). First, we will solve the division and multiplication operations within the parentheses in both the numerator and the denominator, and then perform the addition. Finally, we will divide the simplified numerator by the simplified denominator.
The numerator is \((40.25 \div 5) + (0.07 \times 5)\).
The denominator is \((0.15 \times 8) + (0.18 \div 0.2)\).
Now we have the simplified expression:
\[ \frac{8.40}{2.10} \]To simplify this, we can remove the decimal points by multiplying both numerator and denominator by 100:
\[ \frac{8.40 \times 100}{2.10 \times 100} = \frac{840}{210} \]Now, perform the division:
\[ \frac{840}{210} = 4 \]C) The evaluated expression is 4.
The question asks for the correct definition of 'Alderman' in the context of a municipal corporation. Understanding the structure and terminology of local self-government bodies in India is crucial for answering this question.
Correct Option: C) Nominated members to the corporation
To find the power of the lamp, we need to use the formula that relates power, voltage, and current. The given values are voltage and current, so we will use the formula \(P = V \times I\).
The power (\(P\)) consumed by an electrical device is given by the product of the voltage (\(V\)) across it and the current (\(I\)) flowing through it.
\[ P = V \times I \]Correct Option: A) 60 W is the calculated power of the lamp.
If \( \frac{c}{d} \) + \( \frac{d}{c} \) = 1, then the value of \(\frac{c^3-d^3}{dc^2-cd^2}\) is:
The problem provides an equation relating variables \(c\) and \(d\), and asks for the value of a more complex algebraic expression involving \(c\) and \(d\). The approach involves simplifying the given equation to find a relationship between \(c\) and \(d\), and then simplifying the target expression using algebraic identities and factorization to substitute the derived relationship.
Simplify the given equation:
We are given the equation:
\[ \frac{c}{d} + \frac{d}{c} = 1 \]Combine the fractions on the left side:
\[ \frac{c^2 + d^2}{cd} = 1 \]Multiply both sides by \(cd\):
\[ c^2 + d^2 = cd \]Rearrange the terms to get a standard form:
\[ c^2 - cd + d^2 = 0 \]Simplify the target expression:
We need to find the value of the expression:
\[ \frac{c^3 - d^3}{dc^2 - cd^2} \]Factorize the numerator using the difference of cubes identity, \(a^3 - b^3 = (a-b)(a^2+ab+b^2)\):
\[ c^3 - d^3 = (c-d)(c^2 + cd + d^2) \]Factorize the denominator by taking out the common term \(cd\):
\[ dc^2 - cd^2 = cd(c - d) \]Substitute these factorized forms back into the expression:
\[ \frac{(c-d)(c^2 + cd + d^2)}{cd(c - d)} \]Assuming \(c \neq d\), we can cancel out the \((c-d)\) term from the numerator and the denominator:
\[ \frac{c^2 + cd + d^2}{cd} \]Now, substitute the relationship found in step 4, \(c^2 + d^2 = cd\), into the simplified expression:
\[ \frac{(c^2 + d^2) + cd}{cd} \]\[ \frac{cd + cd}{cd} \]\[ \frac{2cd}{cd} \]Assuming \(cd \neq 0\), we can cancel out \(cd\):
\[ 2 \]D) The value of the expression is 2, as derived from simplifying the given condition and the target expression.
The problem describes a taxi fare structure with a fixed charge and an additional charge per kilometer. We are given the total fare for a certain distance and need to calculate the fare for a different distance. We will first determine the charge per kilometer using the given information and then apply it to find the total charge for the new distance.
The total charge is the sum of the fixed charge and the variable charge (charge per km multiplied by distance).
\[ \text{Total Charge} = \text{Fixed Charge} + (\text{Charge per km} \times \text{Distance}) \]\[ 150 = 40 + (\text{Charge per km} \times 11) \]\[ 150 - 40 = \text{Charge per km} \times 11 \]\[ 110 = \text{Charge per km} \times 11 \]Now, we need to find the total charges paid by Ramesh if he travelled a distance of 20 km, using the fixed charge and the calculated charge per kilometer.
\[ \text{Charges for 20 km} = \text{Fixed Charge} + (\text{Charge per km} \times 20) \]\[ \text{Charges for 20 km} = 40 + (10 \times 20) \]\[ \text{Charges for 20 km} = 40 + 200 \]\[ \text{Charges for 20 km} = \text{Rs } 240 \]D) 240 is the correct answer. The total charge for 20 km is Rs 240, calculated by adding the fixed charge of Rs 40 to the variable charge of Rs 200 (20 km * Rs 10/km).
Using the fact that \(\sqrt{18496}\) = 136, find the value of \(\sqrt{184.96}\) - \(\sqrt{1.8496}\).
The problem asks us to calculate the value of an expression involving square roots of decimal numbers, given the square root of an integer. We will use the given information \(\sqrt{18496} = 136\) and properties of square roots to simplify the terms in the expression \(\sqrt{184.96} - \sqrt{1.8496}\).
We are given that \(\sqrt{18496} = 136\).
We can write \(184.96\) as a fraction:
\[ 184.96 = \frac{18496}{100} \]Now, substitute this into the square root expression:
\[ \sqrt{184.96} = \sqrt{\frac{18496}{100}} \]Using the property \[\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\]:
\[ \sqrt{184.96} = \frac{\sqrt{18496}}{\sqrt{100}} \]Substitute the given value \(\sqrt{18496} = 136\) and calculate \(\sqrt{100} = 10\):
\[ \sqrt{184.96} = \frac{136}{10} = 13.6 \]We can write \(1.8496\) as a fraction:
\[ 1.8496 = \frac{18496}{10000} \]Now, substitute this into the square root expression:
\[ \sqrt{1.8496} = \sqrt{\frac{18496}{10000}} \]Using the property \[\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\]:
\[ \sqrt{1.8496} = \frac{\sqrt{18496}}{\sqrt{10000}} \]Substitute the given value \(\sqrt{18496} = 136\) and calculate \(\sqrt{10000} = 100\):
\[ \sqrt{1.8496} = \frac{136}{100} = 1.36 \]Substitute the simplified values of the two terms:
\[ \sqrt{184.96} - \sqrt{1.8496} = 13.6 - 1.36 \]Perform the subtraction:
\[ 13.60 - 1.36 = 12.24 \]A) 12.24 is the correct answer, as calculated above.