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Standard X

Mathematics

Sphere and Its Surface Area

Assertion :Th...

Question

Assertion :The radius of two spheres are in the ratio $5 : 7$ . The volume of the spheres will be in the ratio $25 : 49$ Reason: The Volume of a sphere is directly proportional to the square of its radius.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is D Both Assertion and Reason are incorrect
Volume of sphere, $V = \frac{4}{3} π r^{3}$
i.e., $V \propto r^{3}$
$∴ \frac{V_{1}}{V_{2}} = {(\frac{r_{1}}{r_{2}})}^{3} = {(\frac{5}{7})}^{3} = \frac{125}{343}$
Hence, option D is correct

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Similar questions

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.

Q. Assertion: The surface are of a sphere is 2464 cm². Its volume is

11498 \frac{2}{3} {cm}^{3} (π = \frac{22}{7}) .

Reason: The volume of a sphere of radius r is

\frac{4}{3} {πr}^{3}

.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Assertion: Be and Al have similar properties.

Reason: $B e^{2 +}$ and $A l^{3 +}$ have nearly the same charge/volume ratios and similar polarising power.

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).

(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).

Q. Assertion: The compressibility factor for

H_{2}

and

H e

(1 + \frac{P b}{R T})

Reason: The compressibility factor for

H_{2}

and

H e

can be derived from Van der Waal's equation.

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Assertion :The radius of two spheres are in the ratio 5:7. The volume of the spheres will be in the ratio 25:49 Reason: The Volume of a sphere is directly proportional to the square of its radius.

The correct option is D Both Assertion and Reason are incorrectVolume of sphere, V=43πr3i.e., V∝r3∴V1V2=(r1r2)3=(57)3=125343Hence, option D is correct

Assertion :The radius of two spheres are in the ratio $5 : 7$ . The volume of the spheres will be in the ratio $25 : 49$ Reason: The Volume of a sphere is directly proportional to the square of its radius.

The correct option is D Both Assertion and Reason are incorrect
Volume of sphere, $V = \frac{4}{3} π r^{3}$
i.e., $V \propto r^{3}$
$∴ \frac{V_{1}}{V_{2}} = {(\frac{r_{1}}{r_{2}})}^{3} = {(\frac{5}{7})}^{3} = \frac{125}{343}$
Hence, option D is correct