Question

Curved surface area of a conical cup is 154root2 cm and base radius is 7 find the angle at the vertex of the conical cup

Answer 1

The vertex angle of cone is 90°

Step-by-step explanation:

Curved surface area of a conical cup $=154\sqrt{2}\ cm^2$

Radius = 7 cm

$\pi rl=154\sqrt{2}$

$\pi\times 7\times l=154\sqrt{2}$

$l=7\sqrt{2}$

Let vertex angle be Ф

$\sin\dfrac{\theta}{2}=\dfrac{r}{l}$

$\sin\dfrac{\theta}{2}=\dfrac{7}{7\sqrt{2}}$

$\sin\dfrac{\theta}{2}=\dfrac{1}{\sqrt{2}}$

$\dfrac{\theta}{2}=45^\circ$

$\theta=90^\circ$

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Answer 2

The angle at the vertex of the conical cup=90 degrees

Step-by-step explanation:

Curved surface area of conical cup=$154\sqrt 2cm^2$

Radius of base=7 cm

Curved surface area of cone=$\pi rl$

Where r=Radius of cone

l=Slant height

$\pi=\frac{22}{7}$

Using the formula

Curved surface area of conical cup=$\frac{22}{7}\times 7\times l$

$154\sqrt 2=22l$

$l=\frac{154\sqrt 2}{22}=7\sqrt 2cm$

In right triangle

$sinx=\frac{perpendicular\;side}{hypotenuse}$

Using the formula

$\frac{r}{l}=sinx$

$\frac{7}{7\sqrt 2}=sinx$

$sinx=\frac{1}{\sqrt 2}=sin45^{\circ}$

$x=45^{\circ}$

Vertex angle of conical cone=2x=$2(45)=90^{\circ}$

Hence, the angle at the vertex of the conical cup=90 degrees

#Learns more:

https://brainly.in/question/2574011:Answered by powersteel