Step-by-step explanation:
as the graphic shows, there are 2 objects : 1 block and 1 triangular shaped half-block.
the block is
7cm × 6cm × 2cm
the half-block is
8cm × 7cm × 6cm
with 10cm being the length of the tilted "roof" area.
the 2 sides facing each other are not visible to the observer, so, they are not part of the surface area of the composite figure.
let's start with the block :
top and bottom 7×2
front and back 6×2
no left (fully covered by the half-block)
right 6×7
that gives us :
2 × 7×2 = 2×14 = 28 cm²
2 × 6×2 = 2×12 = 24 cm²
6×7 = 42 cm²
in total : 94 cm²
the half-block :
top 10×7
bottom 8×7
front and back (triangles) 8×6/2
no left (due to being a half-block)
no right (fully covered by the block)
that gives us :
10×7 = 70 cm²
8×7 = 56 cm²
2 × 8×6/2 = 2×24 = 48 cm²
in total : 174 cm²
so, the complete surface area of the composite figure is
94 + 174 = 268 cm²
Answer:
Dotted line
Step-by-step explanation:
when using the > or < symbols you put a dotted line because the line is not included in the shaded area.
If the symbols were a <u><</u> or a <u>></u> you would put a solid line.
It should be -48. Multiply 40 by the reciprocal and simplify.
x - 2y + z = 5 | *2
⇒ 2x - 4y+ 2z=10
3x + 3y - 2z = - 6 } I sum up these relations
--------------------------------
2x+3x - 4y+3y+2z-2z=10-6
5x - y = 4 (1)
3x + 3y - 2z = - 6 | *3 ⇒ 9x + 9y - 6z = - 18
2x - y + 3z = 11 | *2 ⇒ 4x - 2y + 6z= 22 I sum up these
----------------------------------
⇒ 9x+4x+9y-2y-6z+6z= 4
13x+ 7y= 4 (2)
I write (1) and (2)
5x - y = 4 | *7
35x - 7y= 28
13x+7y=4
48x = 32
x= 32/48=4/6 ( 32:8=4, 48:8=6)
x= 2/3
5x-y=4,
5*2/3-y=4
y=10/3 -4=10/3-12/3=-2/3
⇒ y= - 2/3
x - 2y + z = 5
2/3 - 2*(-2/3)+z=5
2/3+4/3+z=5
6/3+z=5
2+z=5
z=3
x+y+z=2/3-2/3+3=3
x+y+z=3
Answer:
904.78
Step-by-step explanation:
we have the radius, which is 6.
were trying to find the volume.
the foemula for the v of a sphere is 4/3(pi)r^3
so, multiply 4/3 times pi and we get 4.18879.
find 6^3, which is 216. multiply tyese two values, and we get 904.77864.
so, the volume of this sphere is around 904.78
