Question

What is the total surface area of the code?
A) 273 cm2
B) 224 cm2
C) 147 cm2
D) 175 cm2

Answer 1

Hello!

The answer is: None of the options.

The correct answer is: $703.69cm^{2}$

Why?

The total surface area of the cone is equal to:

$TotalArea=BaseArea+LateralArea$

Calculations:

tex]BaseArea=\pi*r^{2}=\pi*7^{2}=153.94cm^{2}[/tex]

$LateralArea=BasePerimeter*SlantHeight/2\\BasePerimeter=2*\pi*r=2*\pi*7=43.98cm\\SlantHeight=\sqrt{height^{2}+radius^{2}  }=\sqrt{576+49}=\sqrt{625}=25$

[$LateralArea=43.98*\frac{25}{2}=549.75cm^{2}$

So,

$TotalArea=153.94cm^{2} +549.75cm^{2}=703.69cm^{2}$

Have a nice day!

Answer 2

Answer:

S.A = 704 cm^2

Step-by-step explanation:

We know that the formula to find the surface area of a cone:

S.A = $\pi r (r + \sqrt{h^2 + r^2} )$, where "r" is the radius and "h" is the height.

Given: r = 7 cm and h = 24 cm. The value of π = 22/7

Now plug in the given values in the above formula, we get

S.A = $= \frac{22}{7} *7 (7 + \sqrt{24^{2}+ 7^2 } )$

S.A = $22(7 + \sqrt{576 + 49} )$

S.A = $22(7 + \sqrt{625} )$

S.A = 22( 7 + 25)

S.A = 22(32)

S.A = 704 cm^2

The surface area of the cone is S.A = 704 cm^2.