Volume of a combination of solids 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. A cone and a cylinder have the same radius and height; the ratio of their volumes is:

• A.1 : 1
• B.1 : 3
• C.1 : 2
• D.3 : 1

Answer: B. 1 : 3

Q3. A cylinder, a cone and a sphere have the same radius; cylinder and cone heights equal 2r. Their volume ratio (cyl:cone:sphere) is:

• A.2 : 1 : 3
• B.3 : 1 : 2
• C.1 : 1 : 1
• D.1 : 2 : 3

Answer: B. 3 : 1 : 2

Reading the problem, 2 (math, chapter 'Surface Areas and Volumes'). Our target: the unknown asked. The principle that connects these is - hence the answer = 3 : 1 : 2. Substituting and simplifying: hence the answer = 3 : 1 : 2. Draw the relevant radii and use the fact that the tangent _|_ radius at the contact point. Matching this against the options, B) 3 : 1 : 2 is the answer. As for the others, option A) '2 : 1 : 3' fails since It is 3:1:2; option C) '1 : 1 : 1' is incorrect: They differ; 3:1:2.