For the given statements, choose the correct option:
Assertion (A): Volume of a hemisphere is $\frac{4}{3} π r^{3} .$
Reason (R): Volume of cone is $\frac{1}{3} π r^{2} .$

(A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(C) Assertion (A) is true but reason (R) is false.

(D) Assertion (A) is false but reason (R) is true.

[1 Mark]

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Solution

Solution:

Option D is the correct answer.
(1 mark)

Volume of a hemisphere is $\frac{2}{3} π r^{3} .$
hence the assertion statement is false.
where as the resion statement is true.
So, option D is the correct answer.

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Similar questions

Q. Assertion (A)
The curved surface area of a cone of base radius 3 cm and height 4 cm is 15π cm².

Reason (R)
Volume of a cone = πr²h

(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:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) 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.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) If ABCD is a rhombus whose one & Median of a triangle divides it angle is 60^{\circ} then the ratio of the & into two triangles of equal area. lenghts of its diagonals is \sqrt{3} : 1. \end{matrix}$

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

This 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) 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.

(a) Both Assertion (A) and Reason (R) are true and Reason (A) and Reason (R). For selecting the correct answer, use the following code :

(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.

$\begin{matrix} Assertion (A) & Reason (R) \sqrt{3} i s a n i r r a t i o n a l n u m b e r . & T h e s u m o f a r a t i o n a l n u m b e r a n d a n i r r a t i o n a l n u m b e r i s a n i r r a t i o n a l n u m b e r . \end{matrix} The correct answer is: (a)/(b)/(c)/(d).$

Q. Assertion (A)
The outer surface of a hemisphere of radius 7 cm is to be painted. The total cost of painting at Rs 5 per cm²is Rs 2300.

Reason (R)
The total surface area of a hemisphere is 3π r².

(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.

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Solution: Option D is the correct answer. (1 mark) Volume of a hemisphere is 23πr3. hence the assertion statement is false. where as the resion statement is true. So, option D is the correct answer.

Solution:

Option D is the correct answer.
(1 mark)

Volume of a hemisphere is $\frac{2}{3} π r^{3} .$
hence the assertion statement is false.
where as the resion statement is true.
So, option D is the correct answer.