Surface Area of a Sphere and Hemisphere MCQs
Practice Surface Area of a Sphere and Hemisphere multiple-choice questions from Surface Areas and Volumes (Class 9 Maths) - tap an answer for instant feedback and a step-by-step solution. Practice the full set free on the RankByte app.
Surface Area of a Sphere and HemisphereQuiz - Solve & Score
Q1. Two spheres have radii in the ratio 2:3. Reasoning through 4πr^2, the ratio of their surface areas is?
- A.4:9
- B.2:3
- C.8:27
- D.4:6
Answer: A. 4:9
Q2. Two spheres have radii in the ratio 3:5. Reasoning through 4πr^2, the ratio of their surface areas is?
- A.9:25
- B.3:5
- C.27:125
- D.6:10
Answer: A. 9:25
Q3. Two spheres have radii in the ratio 1:4. Reasoning through 4πr^2, the ratio of their surface areas is?
- A.1:16
- B.1:4
- C.1:64
- D.2:8
Answer: A. 1:16
We are told: 1; 4; 4; 960; 2. To find: the unknown asked in the stem. Formula - SA ratio = 4π.r1^2 : 4π.r2^2 = r1^2:r2^2 = 1^2:4^2 = 1:16. This is the equation that links the given quantities to the unknown (math, chapter 'Surface Areas and Volumes'). Numerically: SA ratio = 4π.r1^2 : 4π.r2^2 = r1^2:r2^2 = 1^2:4^2 = 1:16. Hence the answer is A) 1:16. Where the distractors go off: option B) '1:4' fails since Surface area scales as the square of the radius; option C) '1:64' misses the point - That cube ratio is for volumes, not surface areas; option D) '2:8' misses the point - Squaring (not doubling) the radius ratio gives the area ratio.
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