A come and a pyramid has equal heights and volumes.if the base area of the pyramid is 154cm2.find the radius of the cone.

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

4 0

Answer:

Radius = 8.575 cm

Step-by-step explanation:

Formula for volume of a pyramid is;

V_p = ½Ah

Where A is area of base and h is height

Also, formula for volume of cone is given as;

V_c = ⅓πr²h

Now, we are told that V_p = V_c and that h is the same for both shapes.

Thus ;

½Ah = ⅓πr²h

h will cancel out to give;

½A = ⅓πr²

Cross multiply to give;

3A/2π = r²

Base area of pyramid is given as 154 cm². Thus;

(3 × 154)/2π = r²

r = √((3 × 154)/2π

r = 8.575 cm

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