Find the values and arrange in increasing order:
(A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is:
(B) If the radius of a cylinder is increased by 20%, while height is increased by 10%, then the percentage increase in the volume of the cylinder:
(C) If each edge of a cube is increased by 20%, then the percentage increase in its surface area is:
(D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is:
Choose the correct order:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (D), (C), (B), (A)
When every length of a solid is multiplied by a factor, an area is multiplied by the square of the factor and a volume by its cube. A 20% increase multiplies a length by 1.2, and a 10% increase by 1.1.
(D) Sphere, radius increased by 10%: volume — 33.1%. The volume \(\frac{4}{3}\pi r^3\) depends on \(r^3\): \(1.1^3=1.331\), an increase of 33.1%.
(C) Cube, each edge increased by 20%: surface area — 44%. The surface area \(6a^2\) depends on \(a^2\): \(1.2^2=1.44\), an increase of 44%.
(B) Cylinder, radius increased by 20% and height by 10%: volume — 58.4%. The volume \(\pi r^2h\) is multiplied by \(1.2^2\times1.1=1.44\times1.1=1.584\), an increase of 58.4%.
(A) Cube, each edge increased by 20%: volume — 72.8%. The volume \(a^3\) is multiplied by \(1.2^3=1.728\), an increase of 72.8%.