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MATH / The figure below consists of four semicircles and the 16-cm diameter of the…

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Answer published by the source. Consult the official source to check your work against its answer.

problem

The figure below consists of four semicircles and the 16-cm diameter of the largest semicircle. What is the total number of square cm in the area of the two shaded regions? Use 3.14 as an approximation for π\pi, and express your answer as a decimal to the nearest tenth. [asy]import graph; size(200); picture p; real h = .25,w = 1,textsize = 10pt,width = 1; filldraw(Arc((8,0),8,0,180)--cycle,gray(.6),black+linewidth(width)); filldraw(Arc((6,0),6,0,180)--cycle,white,black+linewidth(width)); filldraw(Arc((4,0),4,0,180)--cycle,gray(.6),black+linewidth(width)); filldraw(Arc((2,0),2,0,180)--cycle,white,black+linewidth(width)); draw(p,(0,h)--(0,-h)^^(0,0)--(4,0)^^(4,h)--(4,-h),linewidth(width)); fill(p,(w,h)--(4-w,h)--(4-w,-h)--(w,-h)--cycle,white); label(p,"4 cm",(2,0),fontsize(textsize)); add(shift(.5*down)*p); add(shift(4*right)*shift(.5*down)*p); add(shift(8*right)*shift(.5*down)*p); add(shift(12*right)*shift(.5*down)*p);[/asy]
Plain-text mathematical notation (without MathML)
The figure below consists of four semicircles and the 16-cm diameter of the largest semicircle. What is the total number of square cm in the area of the two shaded regions? Use 3.14 as an approximation for π, and express your answer as a decimal to the nearest tenth.

[asy]import graph;
size(200);
picture p;
real h = .25,w = 1,textsize = 10pt,width = 1;
filldraw(Arc((8,0),8,0,180)--cycle,gray(.6),black+linewidth(width));
filldraw(Arc((6,0),6,0,180)--cycle,white,black+linewidth(width));
filldraw(Arc((4,0),4,0,180)--cycle,gray(.6),black+linewidth(width));
filldraw(Arc((2,0),2,0,180)--cycle,white,black+linewidth(width));
draw(p,(0,h)--(0,-h)^^(0,0)--(4,0)^^(4,h)--(4,-h),linewidth(width));
fill(p,(w,h)--(4-w,h)--(4-w,-h)--(w,-h)--cycle,white);
label(p,"4 cm",(2,0),fontsize(textsize));
add(shift(.5*down)*p);
add(shift(4*right)*shift(.5*down)*p);
add(shift(8*right)*shift(.5*down)*p);
add(shift(12*right)*shift(.5*down)*p);[/asy]
Original LaTeX notation
The figure below consists of four semicircles and the 16-cm diameter of the largest semicircle. What is the total number of square cm in the area of the two shaded regions? Use 3.14 as an approximation for $\pi$, and express your answer as a decimal to the nearest tenth.

[asy]import graph;
size(200);
picture p;
real h = .25,w = 1,textsize = 10pt,width = 1;
filldraw(Arc((8,0),8,0,180)--cycle,gray(.6),black+linewidth(width));
filldraw(Arc((6,0),6,0,180)--cycle,white,black+linewidth(width));
filldraw(Arc((4,0),4,0,180)--cycle,gray(.6),black+linewidth(width));
filldraw(Arc((2,0),2,0,180)--cycle,white,black+linewidth(width));
draw(p,(0,h)--(0,-h)^^(0,0)--(4,0)^^(4,h)--(4,-h),linewidth(width));
fill(p,(w,h)--(4-w,h)--(4-w,-h)--(w,-h)--cycle,white);
label(p,"4 cm",(2,0),fontsize(textsize));
add(shift(.5*down)*p);
add(shift(4*right)*shift(.5*down)*p);
add(shift(8*right)*shift(.5*down)*p);
add(shift(12*right)*shift(.5*down)*p);[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
03779fd6-8825-5c30-a073-3c924b4e8a9a
task_key
geometry--test--03779fd6-8825-5c30-a073-3c924b4e8a9a
task_revision_id
1
config / split
geometry / test

Official source

initial import