Question

Please helpp!! thankss

Answer 1

Answer:

A. 7.9989cm

B. 16.5091cm

C. 5502cm3

D.1114.01cm2

Step-by-step explanation:

A. Find the radius of the cylinder.

We know the base of the cylinder is $201cm^2$

We know that the base of a cylinder is a circle

$Area = \pi r^{2}$ for a circle, we know the area so we can work backwards

$201 = \pi r^{2}$

divide by pi

$\frac{201}{\pi} =\frac{\pi r^{2} }{\pi }$

Simplify

$63.9822 = r^2$

Find the square root of each side

$\sqrt{ 63.9822} = \sqrt{r^2}$

7.9989 = r

B. If the volume of the cone is $662cm^3$ find the height

$V = \pi r^{2} \frac{h}{3}$

Plug in and simplify and you will get a height of 16.5091cm

C. C is more complicated but we need to find the volume of the model, then use .5g for density to find the mass.

We must find the volume of the half-sphere on top, the radius is 7.9989, so the volume is 2143.7760

Now we find the volume of the cylinder, use the volume formula to find a volume of

Now add the half-sphere to the cylinder then subtract the cone

$2143.7760 + 4020.1328 - 662 = 5501.9088$

Round and you get 5502cm3

D. Find Surface area if the surface area of the cone is 251

Now we must find the surface area of the half sphere

Use the surface area formula then divide by 2 for a half sphere, this equals 402.01295

Now find the surface are of the slot left behind by the cone

Use the surface area formula and you get 661.9986, now subtract the area of a circle the base size of the cone (201), then you get

Add all three,

$402.01295 + 251 + 460.9986 = 1114.01155$

round to two decimal places

1114.01