MP Board · Class 10 · Mathematics · Surface Areas and VolumesIf the radius of a sphere is doubled, its surface area becomes:
Step-by-Step Solution
The surface area of a sphere of radius $r$ is $S_1 = 4\pi r^2$. When radius becomes $2r$, the new surface area is $S_2 = 4\pi (2r)^2 = 4\pi (4r^2) = 16\pi r^2 = 4S_1$. Thus, it becomes 4 times.
Detailed Options Breakdown
Option : 2 times
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
Option 1: 4 times (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 8 times
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
Option 3: 16 times
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
💡 Study Guide: This question tests core syllabus concepts from Surface Areas and Volumes. For formulas, key summaries, and mock exam reference guides, read the full Surface Areas and Volumes Revision Notes.