Find the volume (in cm3) of a sphere having a diameter of 4.2 cm, giving your answer correct to one place of decimal. Take π = \( \frac{22}{7} \)
To find the volume of a sphere, we need its radius. The problem provides the diameter, so we first calculate the radius. Then, we use the formula for the volume of a sphere and substitute the given values, including the approximation for \(\pi\), to find the volume. Finally, we round the result to one decimal place.
Identify the given information:
Calculate the radius of the sphere:
The radius \((r)\) is half of the diameter.
Recall the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]Substitute the values into the formula:
\[ V = \frac{4}{3} \times \frac{22}{7} \times (2.1)^3 \]\[ V = \frac{4}{3} \times \frac{22}{7} \times (2.1 \times 2.1 \times 2.1) \]\[ V = \frac{4}{3} \times \frac{22}{7} \times 9.261 \]Perform the calculation:
We can simplify the calculation by noting that \(2.1 = \frac{21}{10}\).
\[ V = \frac{4}{3} \times \frac{22}{7} \times \left(\frac{21}{10}\right)^3 \]\[ V = \frac{4}{3} \times \frac{22}{7} \times \frac{21 \times 21 \times 21}{10 \times 10 \times 10} \]\[ V = \frac{4}{3} \times \frac{22}{7} \times \frac{9261}{1000} \]\[ V = 4 \times 22 \times \frac{1}{3} \times \frac{1}{7} \times \frac{9261}{1000} \]\[ V = 88 \times \frac{9261}{21 \times 1000} \]\[ V = 88 \times \frac{441}{1000} \]\[ V = \frac{38808}{1000} \]\[ V = 38.808 \text{ cm}^3 \]Round the answer to one decimal place:
Rounding \(38.808\) to one decimal place gives \(38.8 \text{ cm}^3\).
Correct Option: C) 38.8
The question asks for the investment target set by the Tamil Nadu Space Industrial Policy 2025. This is a factual question related to a specific government policy. To answer correctly, one needs to recall the stated financial goals of this policy.
A) ₹10,000 crore is the correct investment target as per the Tamil Nadu Space Industrial Policy 2025. This figure has been officially announced as part of the policy's objectives to boost the state's space sector.
To solve this series, we need to identify the pattern in each component of the letter-number clusters: the first letter, the second letter, and the number. We will analyze each component separately to find the rule governing its progression.
The first letter is I, the second letter is C, and the number is 59. Therefore, the next cluster in the series is IC59.
Correct Option: A) IC59
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on English alphabetical order. We need to find a consistent rule or relationship between the letters in each pair and then identify the one that deviates.
C) YW – DV — This option does not follow the pattern. The first letter of YW (Y) shifts to the first letter of DV (D) by \(+5\) (Y \(\xrightarrow{+5}\) D, considering wrap-around: Y(25) \(\to\) Z(26) \(\to\) A(1) \(\to\) B(2) \(\to\) C(3) \(\to\) D(4)). However, the second letter of YW (W) shifts to the second letter of DV (V) by \(-1\) (W(23) \(\xrightarrow{-1}\) V(22)). All other options show a \(-2\) shift for the second letter.
The question asks to identify the Indian state with the highest Human Development Index (HDI) in the year 2017. To answer this, one needs to recall or know the HDI rankings of Indian states for that specific period.
A) Kerala had the highest Human Development Index (HDI) in India in 2017. This is a well-established fact, primarily due to its high literacy rates, strong public health system, and high life expectancy.
The question asks for the correct method to save a new workbook in MS Excel. When saving a new file for the first time, you need to specify a file name and location. This is typically done using the "Save As" function.
Correct Option: B) Click the 'File' tab and choose 'Save As'
The question asks for the mascot of Expo 2025 in Osaka. This is a factual question related to current events and major international exhibitions. Identifying the correct mascot requires knowledge of the specific details of Expo 2025.
Correct Option: C) Myaku-Myaku is the official mascot of Expo 2025 in Osaka, Japan. Its distinctive design is based on the Expo's official logo.
This is a logical reasoning problem involving scheduling. We need to determine the exam schedule for seven people (P, Q, R, S, T, U, V) over seven days of a week (Monday to Sunday) based on the given clues. We will use a table to map people to days and deduce the schedule step-by-step.
Initial Setup: Create a table for the days of the week.
| Day | Person |
|---|---|
| Monday | |
| Tuesday | |
| Wednesday | |
| Thursday | |
| Friday | |
| Saturday | |
| Sunday |
Clue 1: Q has an exam on Saturday.
| Day | Person | |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday | ||
| Saturday | Q | |
| Sunday |
Clue 2: P has an exam immediately after V, and R has an exam immediately before V.
This means the sequence is R - V - P. This block of three people must be placed consecutively.
Clue 3: Only 4 people have exams between T and U, neither of whom has an exam on Monday.
If there are 4 people between T and U, and there are 7 days in total, this means T and U must be at the extreme ends of the remaining slots, or close to them. Since neither T nor U is on Monday, let's consider the possible positions for T and U. If T is on Tuesday, U would be on Sunday (4 days between them: Wed, Thu, Fri, Sat). If U is on Tuesday, T would be on Sunday. This is the only way to have exactly 4 people between them without T or U being on Monday.
Clue 4: U has an exam after P.
Combining Clue 2 (R-V-P) and Clue 4 (U after P), we know the sequence R-V-P-U. This means U cannot be on Tuesday because P would have to be on Monday, which is not possible as R-V-P needs 3 consecutive days. Therefore, T must be on Tuesday and U must be on Sunday.
| Day | Person |
|---|---|
| Monday | |
| Tuesday | T |
| Wednesday | |
| Thursday | |
| Friday | |
| Saturday | Q |
| Sunday | U |
Placing R-V-P: We have the sequence R-V-P. The available consecutive slots are Monday, Wednesday, Thursday, Friday. Since Q is on Saturday and U is on Sunday, and T is on Tuesday, the only three consecutive days available are Wednesday, Thursday, Friday. So, R is on Wednesday, V is on Thursday, and P is on Friday.
| Day | Person |
|---|---|
| Monday | |
| Tuesday | T |
| Wednesday | R |
| Thursday | V |
| Friday | P |
| Saturday | Q |
| Sunday | U |
Final Placement: The only person left is S, and the only day left is Monday. So, S has an exam on Monday.
| Day | Person |
|---|---|
| Monday | S |
| Tuesday | T |
| Wednesday | R |
| Thursday | V |
| Friday | P |
| Saturday | Q |
| Sunday | U |
Answer the question: How many people have exams after R?
R has an exam on Wednesday. The people with exams after R are V (Thursday), P (Friday), Q (Saturday), and U (Sunday). There are 4 people.
D) 4. People having exams after R are V, P, Q, and U, which are 4 people.
To find the average weight of the entire group, we need to calculate the total weight of all individuals and divide it by the total number of individuals. Since percentages are given, we can assume a total number of people (e.g., 100) to simplify calculations, or work directly with percentages as proportions.
Determine the proportion of each group:
Calculate the weighted average: The average weight of the group is the sum of (proportion of each group \(\times\) average weight of that group).
\[ \text{Average Weight} = (\text{Proportion of Men} \times \text{Average Weight of Men}) + \]\[ (\text{Proportion of Women} \times \text{Average Weight of Women}) + \]\[ (\text{Proportion of Children} \times \text{Average Weight of Children}) \]Substitute the given values:
Perform the calculations:
The average weight of the group is 42 kg.
C) 42 kg is the correct average weight of the group, calculated by taking the weighted average of the individual group weights.
The question asks to identify the dominant soil type in the Great Plains of India. This requires knowledge of the geographical distribution and formation of major soil types in India.
Correct Option: C) Alluvial soil is the most widespread and dominant soil type in the Great Plains of India. It is formed by the deposition of sediments brought by the Himalayan rivers and is highly fertile, making the plains agriculturally productive.