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

(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.

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

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) I f t h e v o l u m e s o f t w o s p h e r e s a r e & V o l u m e o f a s p h e r e s = \frac{4}{3} π R^{3} . i n t h e r a t i o 27 : 8 t h e n t h e i r s u r f a c e a r e a s a r e i n t h e r a t i o 3 : 2 & S u r f a c e a r e a o f a s p h e r e = 4 π R^{2} . \end{matrix}$

The correct answer is (a) / (b) / (c) / (d).

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Solution

Let $r_{1}$ and $r_{2}$ be the radius of the two spheres.
Volume of sphere of radius $r_{1}$ cm = $\frac{4}{3}$ $\times$ $π$ $\times$ $r_{1}^{3}$
Volume of sphere of radius $r_{2}$ cm = $\frac{4}{3}$ $\times$ $π$ $\times$ $r_{2}^{3}$
Ratio of their volumes = $\frac{V o l u m e o f s p h e r e o f r a d i u s (r_{1}) c m}{V o l u m e o f s p h e r e o f r a d i u s (r_{2}) c m}$
$\frac{27}{8}$ = $\frac{V o l u m e o f s p h e r e o f r a d i u s (r_{1}) c m}{V o l u m e o f s p h e r e o f r a d i u s (r_{2}) c m}$
$\frac{27}{8}$ = $\frac{r_{1}^{3}}{r_{2}^{3}}$
Taking cuberoot on the both sides;
$\frac{r_{1}}{r_{2}}$ = $\frac{3}{2}$
Surface area of sphere $r_{1}$ cm = 4 $\times$ $π$ $\times$ $r_{1}^{2}$
Surface area of sphere $r_{2}$ cm = 4 $\times$ $π$ $\times$ $r_{2}^{2}$
$\frac{S u r f a c e a r e a o f s p h e r e r_{1} c m}{S u r f a c e a r e a o f s p h e r e r_{2} c m}$ = $\frac{9}{4}$

So option d is correct
(d) Assertion (A) is false and Reason (R) is true.

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$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) T h e c u r v e d s u r f a c e a r e a o f a & V o l u m e o f a c o n e = π r^{2} h . c o n e o f b a s e r a d i u s 3 c m a n d h e i g h t 4 c m i s (15 π) c m^{2} . \end{matrix}$

The correct answer is (a) / (b) / (c) / (d).

Q. Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.

Reason (R)
Volume of a sphere =

\frac{4}{3} π R^{3}

Surface area of a sphere =

4 π 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.
(d) Assertion (A) is false and Reason (R) is true.

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

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(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) The diagonals of a | | g m d i v i d e i t & A diagonal of a | | g m d i v i d e s i t i n t o into four triangles of equal area. & two diagonals of equal area. \end{matrix}$

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

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