Assertion and Reason Type Each question consists of two statement… - Vidyadip

MCQ

Assertion and Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Assertion (A)	Reason (R)
If the volumes of two spheres are in the ratio 27 : 8 then their surface areas are in the ratio 3: 2.	Volume of a sphere $=\frac{4}{3}\pi\text{R}^3.$ Surface area of a sphere $=4\pi\text{R}^2.$

A
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
C
Assertion (A) is true and Reason (R) is false.
✓
Assertion (A) is false and Reason (R) is true.

✓

Answer

Correct option: D.

Assertion (A) is false and Reason (R) is true.

Let r and R be the radii of the two sheres.

Ratio of their volumes $=\frac{27}{8}$

$\Rightarrow\frac{\frac{4}{3}\pi\text{r}^3}{\frac{4}{3}\pi\text{R}^3}=\frac{27}{8}$

$\Rightarrow\frac{\text{r}^3}{\text{R}^3}=\frac{27}{8}$

$\Rightarrow\frac{\text{r}}{\text{R}}=\frac{3}{2}$

Ratio of their surface areas $=\frac{4\pi\text{r}^2}{4\pi\text{R}^2}$

$=\Big(\frac{\text{r}}{\text{R}}\Big)^2$

$=\Big(\frac{3}{2}\Big)^2$

$=\frac{9}{4}$

So, the Assertion (A) is false.

The reason (R)s true.

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