On a spherical balloon of 10 cm radius, a circular colour patch has an area of 25 cm². If the balloon is uniformly expanded to a sphere of 50 cm radius, the area of the colour patch in cm² would be
Given:
Initial radius = 10 cm, Final radius = 50 cm, Initial patch area = 25 cm².
Uniform expansion => all linear dimensions scale by the same factor.
Formula:
Area scales with the square of the linear scale factor:
New area = Old area × (R₂/R₁)²
Solution:
Scale factor = 50/10 = 5
New area = 25 × 5² = 25 × 25 = 625 cm²
Correct Answer: (b) 625
A man on a cycle is travelling on a terrain whose height (h) vs distance (d) can be described by a function in a certain unit (h can be negative). Starting at d = 0, the cycle will have the maximum velocity without pedaling at:
Which of the following is true?
If any 9 papers are drawn from a both side printed book, the sum of their page numbers can NEVER be ______.
Average age of 20 students of a class is 10 years. Average age of these students together with their five teachers is 14. The age of Ramesh Sir, one of their five teachers, is exactly the same as the average age of all their five teachers. The sum of the ages (in years) of all the students and Ramesh Sir is
The sixth largest three-digit odd number among those with all digits distinct is
On a spherical balloon of 10 cm radius, a circular colour patch has an area of 25 cm². If the balloon is uniformly expanded to a sphere of 50 cm radius, the area of the colour patch in cm² would be
A fresh water tap fills a fish tank in 40 minutes. The same tank is filled by a salt water tap in 120 minutes. If both the taps are open, how many minutes will it take to fill the tank?
∛0.99 is closest to
The areas (in km²) under forests in four countries A, B, C and D for the years 2014 and 2024 are shown in the given bar chart:
The minimum percentage of deforestation during 2014-2024 was in country
If there is rainfall in a village, flowers will bloom. If flowers bloom, celebrations will definitely take place. Flowers did not bloom. Which of the following is certain?
