If each square of the grid below is $0.5\text{ cm}$ by $0.5\text{ cm}$, how many square centimeters are in the area of the blue figure? [asy]
unitsize(0.5cm);
path p=(1,0)--(1,1)--(2,1)--(2,2)--(1,2) --(1,3)--(0,3)--(0,5)--(1,5)--(1,4) --(2,4)--(2,6)--(3,6)--(3,5)--(6,5) --(6,6)--(7,6)--(7,4)--(8,4)--(8,5) --(9,5)--(9,3)--(8,3)--(8,2)--(7,2) --(7,1)--(8,1)--(8,0)--(6,0)--(6,1) --(3,1)--(3,0)--cycle;
fill(p, blue);
draw(p, black+2);
for(int i=0; i<10; i+=1){ draw((i,0)--(i,6),black+0.6); };
for(int j=0; j<7; j+=1){ draw((0,j)--(9,j),black+0.6); };
[/asy]

8.50 cm²

Step-by-step explanation:

The dimension of each square is given as 0.5cm by 0.5cm

The area of the a square is, a²

Where, a = side length

Area of each square = 0.5² = 0.25cm

The number of blue colored squares = 34

The total area of the blue colored squares is :

34 * 0.25 = 8.50cm²

the answer is the third / last answer

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.