The base radius of a cone is 21 cm and the height is 28 cm, then, which of the following is/are correct?
(A) Slant height = 35 cm
(B) Slant height = 33 cm
(C) Volume = 12936 cm3
(D) Curved Surface Area = 2310 cm2
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C), (D) and (A) only
For a cone of radius \(r\) and height \(h\), the slant height \(l\) is the hypotenuse of the right triangle formed by \(r\) and \(h\), so \(l=\sqrt{r^2+h^2}\); the volume is \(\frac{1}{3}\pi r^2h\) and the curved surface area is \(\pi rl\). Here \(r=21\) cm and \(h=28\) cm.
(A) Slant height = 35 cm Correct.
\(l=\sqrt{21^2+28^2}=\sqrt{441+784}=\sqrt{1225}=35\) cm
(B) Slant height = 33 cm Incorrect. The slant height has only one value, 35 cm, as worked out in (A).
(C) Volume = 12936 cm3 Correct.
\(\displaystyle V=\frac{1}{3}\times\frac{22}{7}\times21\times21\times28\)
\(V=22\times21\times28=12936\) cm3
(D) Curved Surface Area = 2310 cm2 Correct.
\(\displaystyle \mathrm{CSA}=\frac{22}{7}\times21\times35\)
\(\mathrm{CSA}=22\times3\times35=2310\) cm2