Question

(Score for Question 3: ___ of 7 points)
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

Answer:

Answer 1

This isn't a bad problem to do. \[Volume of sphere:V=r ^{3}4\pi\]\[Volume of cone:V=\pi \frac{ h }{ 3 }r ^{3}\]
The only unknowns we have are the radius and height. Luckily, both are given to us. The height for the cone is 14 in. The radius is also very easy to find. Simply divide the diameters by 2 to find the radius. Now plug in the values to solve for volume. Then add them together.

Answer 2

Oh my bad, the radius was already given, so the radius is 9 in.

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @InsatiableSuffering
This isn't a bad problem to do. \[Volume of sphere:V=r ^{3}4\pi\]\[Volume of cone:V=\pi \frac{ h }{ 3 }r ^{3}\]
The only unknowns we have are the radius and height. Luckily, both are given to us. The height for the cone is 14 in. The radius is also very easy to find. Simply divide the diameters by 2 to find the radius. Now plug in the values to solve for volume. Then add them together.
\(\color{#0cbb34}{\text{End of Quote}}\)
COrrection: Volume of sphere needs to be multiplied by 1/3

Answer 4

And because we only have half of a sphere, the volume of a sphere is divided by 2.

Answer 5

Doing the math, I found the volume to be 12214.5 in cubed.

Answer 6

thx so muchj

Answer 7

@InsatiableSuffering

ATTENTION please formula for volume of a sphere not is correct !!!!!!!

you missed divide it by 3

V_sphere = (4pi*r^3)/3

Answer 8

@InsatiableSuffering

and so formula for volume of a cone what you ve wrote above not is correct

V_cone = (pi*r^2 *h )/3

Answer 9

@jhonyy9 I appreciate the correction for the volume of a cone. However, I quoted my post and said the volume of a sphere needed to be multiplied by 1/3. But again, thanks for having my back.