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Surface Area And Volume of A Right Circular Cone [NEW] — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Area And Volume of A Right Circular Cone [NEW]1 Mark
MCQ
Statement-1 (A): A cylinder and a right circular cone have the same base and same height. If the volume of the cone is 25 cubic units, then the volume of the cylinder is 75 cubic units.
Statement-2 (R) : A cylinder and a right circular cone have the same base and same height. The volume of the cylinder is three times the volume of the cone.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
✓

Answer

Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(a)
Let r be the radius of the common base and h be the height of the cylinder as well as that of cone. Then,
$V_1=\text { Volume of the cylinder }=\pi r^2 h, V_2=\text { Volume of the cone }=\frac{1}{3} \pi r^2 h$
Clearly, $V_1=3 V_2$. So, statement- 2 is true.
Replacing $V_2=25$ in $V_1=3 V_2$, we obtain $V_1=75$ cubic units.
So, statement-1 is true. Clearly, statement-2 is a correct explanation for statement-1.

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