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The radius of the base of a cylinder is increased by 10%. At the same time, the height of the cylinder is decreased by x%. Given that the volume of the cylinder remains unchanged, find the value of x.
Let original radius and height be r and h, so initial volume is V = πr²h. The increased radius is r' = 1.1r. Since the volume remains unchanged, π(1.1r)²h' = πr²h, giving 1.21h' = h or h' = h / 1.21. The percentage decrease in height is x = [(h − h') / h] × 100 = [1 − (1 / 1.21)] × 100 = 2100/121% ≈Read more
Let original radius and height be r and h, so initial volume is V = πr²h. The increased radius is r’ = 1.1r. Since the volume remains unchanged, π(1.1r)²h’ = πr²h, giving 1.21h’ = h or h’ = h / 1.21. The percentage decrease in height is x = [(h − h’) / h] × 100 = [1 − (1 / 1.21)] × 100 = 2100/121% ≈ 17.36%.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 14 Math of Space: Surface Area and Volume Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-14/
See lessSmall-group project: Make a group of 3–4 students. Choose one scenario to design a custom rating scheme by assigning appropriate weights: (a) shopping experience at a cloth store, (b) travel experience in a bus, (c) tourism experience of a nearby tourist spot, (d) clinic/hospital experience. (i) Discuss and arrive at 4–6 aspects to rate. For each aspect chosen, justify why it matters for an overall experience. (ii) Discuss and decide the relative weights and justify. (iii) Collect or imagine ratings from at least 10 people on a scale of 1–5 (5 being very good). (iv) Compute each individual rating. Compute the overall average across individuals. (v) Make a 100% stacked bar chart using your data. (vi) Write a short note on the observations and inferences, what your rating system captures well and what it misses.
For scenario (d), evaluate hospital experience using doctor care (weight 4), cleanliness (weight 3) and wait time (weight 2). Gather 1-to-5 ratings from ten respondents and calculate each person's weighted score using formula Σ(wᵢxᵢ) / Σwᵢ. Display the proportion of star ratings across parameters usRead more
For scenario (d), evaluate hospital experience using doctor care (weight 4), cleanliness (weight 3) and wait time (weight 2). Gather 1-to-5 ratings from ten respondents and calculate each person’s weighted score using formula Σ(wᵢxᵢ) / Σwᵢ. Display the proportion of star ratings across parameters using a 100% stacked bar chart, observing service strengths while noting that subjective individual expectations remain uncaptured.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-10/
See lessWhole class project: Each student shares the average age of their family and the number of family members. Discuss among the class and come up with a way to find out the average age of all the families of the class.
A simple average of the family averages is incorrect because family sizes vary. Instead, calculate the weighted average. Each student multiplies their family's average age by their total family member count to determine total family years. Sum these total years across the entire class, then divide bRead more
A simple average of the family averages is incorrect because family sizes vary. Instead, calculate the weighted average. Each student multiplies their family’s average age by their total family member count to determine total family years. Sum these total years across the entire class, then divide by the aggregate number of people across all families combined.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-10/
See lessGiven some data with corresponding weights, what would happen to the weighted average if all the weights are increased by a constant value, say 1? If required, experiment with some data. What do you observe? Justify your answer using algebra.
The weighted average shifts toward the unweighted arithmetic mean. Algebraically, the new mean is Σ(wᵢ + 1)xᵢ / Σ(wᵢ + 1) = [Σwᵢxᵢ + Σxᵢ] / [Σwᵢ + n]. This expression represents a blend of the original weighted mean and the unweighted sum of values. Adding a constant flattens the relative ratio betwRead more
The weighted average shifts toward the unweighted arithmetic mean. Algebraically, the new mean is Σ(wᵢ + 1)xᵢ / Σ(wᵢ + 1) = [Σwᵢxᵢ + Σxᵢ] / [Σwᵢ + n]. This expression represents a blend of the original weighted mean and the unweighted sum of values. Adding a constant flattens the relative ratio between weights, pulling the final average closer to the simple mean.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-10/
See lessA farm has some cows, sheep and chickens. Last year the cows made up 60%, the sheep 25% and the chickens 15%. There was a decrease in the number of all three animals’ population over the year. Choose the possibilities for the change in their respective shares of the population— (i) % of cows decreased, % of sheep decreased, % of chickens decreased (ii) % of cows increased, % of sheep increased, % of chickens increased (iii) % of cows remained the same, % of sheep remained the same, % of chickens remained the same (iv) % of cows decreased, % of sheep increased, % of chickens remained the same (v) % of cows increased, % of sheep increased, % of chickens decreased.
The valid possibilities are (iii), (iv) and (v). Since individual shares must sum to 100%, they cannot all decrease (i) or all increase (ii) simultaneously. If all three populations drop by the same proportion, their shares remain unchanged (iii). If they decrease at different rates, some percentageRead more
The valid possibilities are (iii), (iv) and (v). Since individual shares must sum to 100%, they cannot all decrease (i) or all increase (ii) simultaneously. If all three populations drop by the same proportion, their shares remain unchanged (iii). If they decrease at different rates, some percentage shares will rise while others fall, making statements (iv) and (v) fully attainable.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-10/
See less