Surface Areas and Volumes MCQs

Q1. If a cone is melted and recast into a sphere, what stays the same?

• A.the height
• B.the surface area
• C.the radius
• D.the volume

Answer: D. the volume

To see why, recall that Write the appropriate volume/surface-area formula for the named solid (cube, cuboid, cylinder, cone, sphere, hemisphere or frustum); substitute the given dimensions => the chosen quantity reduces to a single numeric value; hence the required answer = the volume. That fits the listed correct option directly - Correct. Quickly on the wrong ones: option A) 'the height' misses the point - Shape changes; volume is conserved; option B) 'the surface area' misses the point - Recasting conserves volume, not surface. Hence the answer is D) the volume.

Q2. How many cones (radius 2 cm, height 4 cm) can be made by melting a sphere of radius 6 cm?

• A.27
• B.6
• C.54
• D.55

Answer: C. 54

Reading the problem, 2 cm, 4 cm, 6 cm (math, chapter 'Surface Areas and Volumes'). Our target: How many cones (radius 2 cm, height 4 cm) can be made by melting a sphere of radius 6 cm?. The principle that connects these is - hence the answer = 54. Substituting and simplifying: hence the answer = 54. Draw the relevant radii and use the fact that the tangent _|_ radius at the contact point. That lands on option C) 54. As for the others, option A) '27' is wrong because Wrong: uses an incorrect intermediate value; option B) '6' is wrong because Wrong: a common multi-step slip gives this.

Q3. How many cones (radius 2 cm, height 9 cm) can be made by melting a sphere of radius 6 cm?

• A.12
• B.24
• C.25
• D.6

Answer: B. 24

Given 2 cm, 9 cm, 6 cm, asked for How many cones (radius 2 cm, height 9 cm) can be made by melting a sphere of radius 6 cm?. By hence the answer = 24. hence the answer = 24. draw the relevant radii and use the fact that the tangent _|_ radius at the contact point. Hence option B) 24. Others fail: option A) '12' doesn't hold - Wrong: uses an incorrect intermediate value; option C) '25' is wrong because Wrong: a step was skipped or HCF/LCM swapped.