Download App

Maths Assertion (A) & Reason (B) MCQ

Surface Area And Volume of Sphere · CBSE STD 9 (CBSE - English Medium). 8 questions.

Questions

Assertion (A) & Reason (B) MCQ

🎯

Test yourself on this topic

8 questions · timed · auto-graded

MCQ 11 Mark
Statement-1 (A): If a right circular cylinder just encloses a sphere, then surface area of the sphere is equal to the curved surface area of the cylinder.
Statement-2 (R): The volume of the largest sphere that can be inserted in a cube of edge a is $\frac{\pi a^3}{6}$.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-3
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: B.
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-3
(b)
Let the radius of the sphere be r. Then, radius of the cylinder is also r and height of the cylinder is 2r.
$\therefore \quad$ Surface area of sphere $=4 \pi r^2$ and, Surface area of cylinder $=2 \pi r \times 2 r=4 \pi r^2$
Clearly, surface area of the sphere is same as the curved surface area of the cylinder. So, statement-1 is true.
The diameter of the largest sphere that can be inserted in a cube of edge $a$ is equal to $a$. So,
$\text { Volume of the sphere }=\frac{4}{3} \pi\left(\frac{a}{2}\right)^3=\frac{\pi}{6} a^3$
So, statement-2 is true. Hence, option (b) is correct.
View full question & answer→
MCQ 21 Mark
Statement-1 (A): If the surface areas of two spheres are in the ratio $9: 25$, then their radii are in the ratio $3: 5$.
Statement-2 (R) : If surface areas of two spheres are in the ratio $S_1: S_2$, then their radii are in the ratio $\sqrt{S_1}: \sqrt{S_2}$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-2
  • 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-2
(a)
Let $r_1, r_2$ be the radii of two spheres. Then,
$S_1=4 \pi r_1^2$ and $S_2=4 \pi r_2^2 \Rightarrow \frac{S_1}{S_2}=\frac{4 \pi r_1^2}{4 \pi r_2^2} \Rightarrow \frac{S_1}{S_2}=\left(\frac{r_1}{r_2}\right)^2 \Rightarrow \frac{r_1}{r_2}=\frac{\sqrt{S_1}}{\sqrt{S_2}}$$\quad$...(i)
So, statement-2 is true.
Replacing $S_1$ by 9 and $S_2$ by 25 in (i), we obtain $\frac{r_1}{r_2}=\frac{3}{5}$.
So, statement- 1 is also true.
Also, statement-2 is a correct explanation for statement-1. Hence, option (a) is correct.
View full question & answer→
MCQ 31 Mark
Statement-1 (A): If the ratio of volumes of two spheres is 27 : 64, then the ratio of their surface areas is 9 : 16.
Statement-2 (R): If $V_1, V_2$ are volumes and $S_1, S_2$ are surface areas of two spheres, then
$\frac{S_1}{S_2}=\left(\frac{V_1}{V_2}\right)^{2 / 3}$
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
(a)
Let the radii of two spheres be $r_1, r_2$. Then,
$\begin{aligned}& S_1=4 \pi r_1^2, S_2=4 \pi r_2^2, V_1=\frac{4}{3} \pi r_1^3 \text { and } V_2=\frac{4}{3} \pi r_2^3 \\
\Rightarrow \quad & \frac{S_1}{S_2}=\frac{r_1^2}{r_2^2} \text { and } \frac{V_1}{V_2}=\frac{r_1^3}{r_2^3}\end{aligned}$
$\Rightarrow \quad\left(\frac{S_1}{S_2}\right)^{1 / 2}=\frac{r_1}{r_2}$ and $\left(\frac{V_1}{V_2}\right)^{1 / 3}=\frac{r_1}{r_2} \Rightarrow\left(\frac{S_1}{S_2}\right)^{1 / 2}=\left(\frac{V_1}{V_2}\right)^{1 / 3} \Rightarrow \frac{S_1}{S_2}=\left(\frac{V_1}{V_2}\right)^{2 / 3}$$\quad$...(i)
So, statement-2 is true. Replacing $\frac{V_1}{V_2}$ by $\frac{27}{64}$ in (i), we obtain
$\frac{S_1}{S_2}=\left(\frac{27}{64}\right)^{2 / 3}=\left\{\left(\frac{3}{4}\right)^3\right\}^{2 /3}=\frac{9}{16}$
So, statement-1 is also true. Also, statement-2 is a correct explanation for statement-1. Hence, option (a) is correct.
View full question & answer→
MCQ 41 Mark
Statement-1 (A): If the ratio of the surface areas of two spheres is 4: 25, then the ratio of their radii is 4: 5.
Statement-2 (R): If the ratio of radii of two spheres is 2: 3, then the ratio of their volumes is 8:27.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: D.
Statement-1 is false, Statement-2 is true.
d
View full question & answer→
MCQ 51 Mark
Statement-1 (A): If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is $6: \pi$.
Statement-2 (R): The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is 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: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
b
View full question & answer→
MCQ 61 Mark
Statement-1 (A): The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter of the base are equal to the diameter of the sphere.
Statement-2 (R): If a hemisphere and a cylinder stand on equal bases and have the same height, then their volumes are in the ratio 3: 2.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: C.
Statement-1 is true, Statement-2 is false.
c
View full question & answer→
MCQ 71 Mark
Statement-1 (A): If the volumes of two spheres are in the ratio 27: 125, then their radii are in the ratio 3:5.
Statement-2 (R): If the volumes of two spheres are in the ratio $V_1$, $V_2$ then their radii are in the ratio $V_1^{1 / 3}: V_2^{1 / 3}$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is 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 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
View full question & answer→
MCQ 81 Mark
Statement-1 (A): If the ratio of the surface areas of two spheres is 4: 9, then the ratio of their volumes is 8: 27.
Statement-2 (R): The volumes $V_1$, $V_2$ and surface areas of two sphere are connected by the relation $\left(\frac{S_1}{S_2}\right)^3=\left(\frac{V_1}{V_2}\right)^2$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is 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 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
View full question & answer→
Generate Paper FreeAll Surface Area And Volume of Sphere topics
Assertion (A) & Reason (B) MCQ - Maths STD 9 Questions - Vidyadip