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.

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Solution

(c) Assertion (A) is true and Reason (R) is false.
Assertion (A):
Curved surface area of a cone $= π r \sqrt{r^{2} + h^{2}}$
$= π \times 3 \times \sqrt{{(3)}^{2} + {(4)}^{2}} = π \times 3 \times \sqrt{9 + 16} = π \times 3 \times \sqrt{25} = 15 π {cm}^{2}$
Hence, Assertion (A) is true.

Reason (R): The given statement is false.

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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 (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.

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.

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

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

Q. Assertion: The curved surface area of a cone is 550 cm² and its diameter is 14 cm. Then, its slant height is 25 cm.
Reason: The curved surface area of a cone having base radius r and slant height l is πrl.
(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.

Q. Assertion (A)
The area of the quadrant of a circle having a circumference of 22 cm is

9 \frac{5}{8} {cm}^{2} .

Reason (R)
The area of a sector of a circle of radius r with central angle x° is

(\frac{x \times π r^{2}}{360}) .

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) Reason (R) 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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(c) Assertion (A) is true and Reason (R) is false. Assertion (A): Curved surface area of a cone=πrr2+h2 =π×3×32+42=π×3×9+16=π×3×25=15π cm2 Hence, Assertion (A) is true. Reason (R): The given statement is false.