The base diameter of a cylinder is 21 cm and the height is 28 cm, the…

The correct answer is Option (2) → (A), (C) and (D) only

For a cylinder of radius \(r\) and height \(h\), volume \(=\pi r^2h\), curved surface area \(=2\pi rh\) and total surface area \(=2\pi r(r+h)\). The question gives the diameter, so the radius is found first.

• Diameter \(=21\,\mathrm{cm}\), so radius \(r=\frac{21}{2}=10.5\,\mathrm{cm}\)

• Height \(h=28\,\mathrm{cm}\)

(A) Radius of cylinder = 10.5 cm Correct. The radius is half the diameter, \(21\div2=10.5\,\mathrm{cm}\).

(B) Volume = 12936 cm³ Incorrect. The volume works out to 9702 cm³, not 12936 cm³:

• \(\displaystyle V=\frac{22}{7}\times\frac{21}{2}\times\frac{21}{2}\times28\)

• \(\displaystyle V=22\times\frac{21}{2}\times\frac{21}{2}\times4=9702\,\mathrm{cm^3}\)

The figure 12936 cm³ is what one gets by interchanging the diameter and the height (radius 14 cm, height 21 cm): \(\frac{22}{7}\times14\times14\times21=12936\).

(C) Curved Surface Area = 1848 cm² Correct.

• \(\displaystyle 2\pi r=2\times\frac{22}{7}\times\frac{21}{2}=66\)

• \(\mathrm{CSA}=2\pi rh=66\times28=1848\,\mathrm{cm^2}\)

(D) Total surface area = 2541 cm² Correct.

• \(\mathrm{TSA}=2\pi r(r+h)=66\times(10.5+28)\)

• \(\mathrm{TSA}=66\times38.5=2541\,\mathrm{cm^2}\)