Easy math problems!
#8 and #10

8. volume of cylinder is pi*r^2*h So V= pi * (radius)^2 * height =720* pi we know circumference = 2 * pi * r if we look at first equation. We can edit it like pi * r * r * h now we can say it kind of looks like circumference equation but missing 2 so we multiply both sides by 2 2 * pi * r * r * h = 2 * 720 * pi We can take out the 2 * pi * r and put in circumference (C) c * r * h = 1440 * pi We we know h is 20 so c * r * 20 = 1440 * pi c * r = 72 * pi we have to solve for r first so break circumference back up 2 * pi * r * r = 72 * pi r * r = 36 r = 6 plug into circum equation C = 2 * pi * 6 C = 12 * pi

10.the cylinders fill uo the box and if radius is 1.5 then diameter is 3. There are 5 in a row some 3 * 5 = 15 box length.

2 in a column so 2 * 3 = 6 box width

the height is 5

So

l * h * w = V

6 * 5 * 15 =V

V = 450

correct answer:

i^31 = -i

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b