i have 2 MATH questions.. that i totaly dont know the answe too CAN U HELP!?

Question

the volume of a cube is 125 in^3. find the surface area.

a. 25 in^2
b. 150 in^2
c. 100 in^2
d. 625 in^2

and this one!

in which way can a plane intersect a sphere?
a. a circle only
b. a line only
c. a point only
d. a point or a circle

HOW ABOUT THIS one... HELP plz

find the surface area of a sphere with a radius of 5 inches...

a. 100pi in^2
b. 166 2/3 pi in^2
c. 50 pi in^2
d. 38 1/2 pi in^2

Answer 1

a. 25 in^2
V=r^3, so r = 5
A = r^2 = 5^2 = 25

d. a point or a circle
if the plane is tangent to the sphere (goes along the outside of the sphere so that it only shares one point), then it intersects as a point. If it intersects though the sphere, the intersection is a circle.

SA of a sphere = 4/3 * pi * r^2
So 4/3 * pi * 5^2 = 100/3 pi in^2
The correct answer is not an option.

Answer 2

For Problem #1
For a cube, V = x³, where x is the dimension of the edges (all the same in a cube). So,
125 = x³
5 = x (take the cube root of both sides).
Now, the surface area formual for a cube is SA = 6x².
Since x = 5, the surface area would be 6(5)² = 150 in².
The answer is B

For Problem #2
The plane could slice through the sphere, creating a circle. Or the sphere could rest atop the plane (still considered an intersection). This would be a point. So the answer is D.

For Problem #3
The surface area formula for a sphere is SA = 4*pi*r².
So SA = 4*pi*(5)²
SA = 100pi in²
The answer is A

Answer 3

the volume of a cube is 125 in^3. find the surface area.

a. 25 in^2
b. 150 in^2
c. 100 in^2
d. 625 in^2

the volume of a cube is given as length x width x height.
the surface area of a cube is 6 times area of square.

since the volume is given,　we can get the single side of the cube by obtaining the cube root of 125, which is 5.

with that in hand, let's solve for the surface area as 6 times 5 times 5 which would equal to 150 inches squared. so it is B.




find the surface area of a sphere with a radius of 5 inches...

a. 100pi in^2
b. 166 2/3 pi in^2
c. 50 pi in^2
d. 38 1/2 pi in^2

hey, I think you can do this one on your own. first, go find for the formula of surface area of sphere then just subtitute 5 for the radius part. I know you can do it and I don't want to spoil everything,coz you won't learn if I do.


Good Luck!

Answer 4

#1 volume is L*H*W in this case. 5*5*5=125. Area is L*H 5*5=25, but this has 6 sides, so 6*25=125in^2 "B"

#2 a sphere is like and apple and the plane is like a knife that is cutting through it. the shape would be "a" circle only.

#3 surface area=4(pi)r^2. thus, (pi)4*5^2 =100piin^2 "A"