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MATH / The lateral surface area of the frustum of a solid right cone is the product of…

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problem

The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height (LL) and the sum of the circumferences of the two circular faces. What is the number of square centimeters in the total surface area of the frustum shown here? Express your answer in terms of π\pi. [asy] draw( scale(1,.2)*arc(origin,10,180,360) ) ; draw( scale(1,.2)*arc(origin,10,15,165) , dashed ) ; //yes, there is a gap draw( (-10,0)--(10,0) , dotted ) ; label("20cm",(0,0),S); draw((0,0)--(0,8)); label("8cm",(0,4),E); draw( shift(0,8)*scale(1,.2)*circle(origin,4) ) ; draw( (-4,8)--(4,8) , dotted ) ; label("8cm",(0,8),N); draw((-10,0)--(-4,8)); draw((10,0)--(4,8)); label("LL",(5,4),NE); [/asy]
Plain-text mathematical notation (without MathML)
The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height (L) and the sum of the circumferences of the two circular faces. What is the number of square centimeters in the total surface area of the frustum shown here? Express your answer in terms of π.

[asy]
draw( scale(1,.2)*arc(origin,10,180,360) ) ;
draw( scale(1,.2)*arc(origin,10,15,165) , dashed ) ; //yes, there is a gap
draw( (-10,0)--(10,0) , dotted ) ;
label("20cm",(0,0),S);
draw((0,0)--(0,8));
label("8cm",(0,4),E);
draw( shift(0,8)*scale(1,.2)*circle(origin,4) ) ;
draw( (-4,8)--(4,8) , dotted ) ;
label("8cm",(0,8),N);
draw((-10,0)--(-4,8));
draw((10,0)--(4,8));
label("L",(5,4),NE);
[/asy]
Original LaTeX notation
The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height ($L$) and the sum of the circumferences of the two circular faces. What is the number of square centimeters in the total surface area of the frustum shown here? Express your answer in terms of $\pi$.

[asy]
draw( scale(1,.2)*arc(origin,10,180,360) ) ;
draw( scale(1,.2)*arc(origin,10,15,165) , dashed ) ; //yes, there is a gap
draw( (-10,0)--(10,0) , dotted ) ;
label("20cm",(0,0),S);
draw((0,0)--(0,8));
label("8cm",(0,4),E);
draw( shift(0,8)*scale(1,.2)*circle(origin,4) ) ;
draw( (-4,8)--(4,8) , dotted ) ;
label("8cm",(0,8),N);
draw((-10,0)--(-4,8));
draw((10,0)--(4,8));
label("$L$",(5,4),NE);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
3b00f6e6-1b0f-569a-9566-3123de620ab8
task_key
geometry--test--3b00f6e6-1b0f-569a-9566-3123de620ab8
task_revision_id
1
config / split
geometry / test

Official source

initial import