)A conical-shaped lampshade has a height of 18 centimeters and a slat height of 19.5 centimeters. Find the volume of the lampshade .

Question

)A conical-shaped lampshade has a height of 18 centimeters and a slat height of 19.5 centimeters. Find the volume of the lampshade .

2)Find the volume of a cylinder that a height of 7 and a diagonal length of 10

Answer 1

draw a cone with the height and the slant height

the height, the slant height, and the radius of the circle form a right triangle

one leg is the height, 18 cm, and the hypotenuse is the slant height, 19.5 cm

the radius is the other leg and it is the unknown, call it r

r^2+18^2=19.5^2

r^2+324=380.25

r^2=380.25-324

r^2=56.25

r=√56.25

r=7.5 cm

now find the volume of the cone using V=(1/3)(∏)(r^2)(h)

V=(1/3)(3.14159)(56.25)(18)

V=(3.14159)(56.25)(6)

V=(3.14159)(337.5)

V=1060.2866 cubic centimeters

 

for #2 do you mean diameter or diagonal ?

if you mean diagonal, then find the diameter the same way as above and take half to get the radius

 

if you mean diameter, take half to get the radius and use the formula...

V=∏*r^2*h