Assertion :If the height of a cone is $24$ cm and diameter of the base is $14$ cm, then the slant height of the cone is $15$ cm. Reason: If $r$ be the radius and $h$ be the height of the cone, then slant height $= \sqrt{h^{2} + r^{2}}$

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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Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
We know that slant height $= l = \sqrt{h^{2} + r^{2}}$
So reason is true,.
Now it is given that height $= h = 24$ cm, diameter $= 14$ cm
$∴$ radius $= r = \frac{d}{2} = \frac{14}{2} = 7$ cm
$∴ l = \sqrt{(24)^{2} + 7^{2}} = 25$
Assertion is false .
So, option D is correct.

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Similar questions

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: The base radius of a cone is 7 cm and its slant height is 25 cm. The volume of the cone is 1232 cm³.
Reason: The volume of a right circular cone of base radius r and height h is

\frac{1}{3} π r^{2} h

.
(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 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.

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 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 :If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm. Reason: If r be the radius and h be the height of the cone, then slant height =√h2+r2

The correct option is D Assertion is incorrect but Reason is correctWe know that slant height =l=√h2+r2So reason is true,.Now it is given that height =h=24 cm, diameter=14 cm∴ radius =r=d2=142=7 cm∴l=√(24)2+72=25Assertion is false .So, option D is correct.

Assertion :If the height of a cone is $24$ cm and diameter of the base is $14$ cm, then the slant height of the cone is $15$ cm. Reason: If $r$ be the radius and $h$ be the height of the cone, then slant height $= \sqrt{h^{2} + r^{2}}$