Acone has a volume of 423pi cm^3 and height of 9cm. calculate the surface area of the cone.

1328.43cm³

Step-by-step explanation:

The equation for the volume is V=(πr²h)÷3

The equation for the surface area is SA=πr²+πrl

First solve for the radius using the volume:

423πcm³=πr²+πr×9

After solving this, the 2 possible x values will be -25.55 and 16.55

Since you can't have a negative surface area, the only option will be 16.55

Now your radius is 16.55 and the slant height is 9

π(16.55)²+π(16.55)×9

The surface area will be 1328.43cm³

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.