- 4 containers.Remember that the given measurement of 4 inches
wide is equal to the diameter of the cylinder. You need to take half
this measurement in order to determine the radius. The volume of
each container is π(2 in.)^2 (4 in.), or 16πcubic inches. One bag fills
the volume of two containers. Two bags will fill the volume of four
containers. - 1,512πin^3. First find the volume of the larger vase, using a radius
of 4: V= (π 42 )(18) = 288πin^3. Next find the volume of the smaller
vase, using a radius of 3: V= (π 32 )(18) = 162πin^3. Subtract these
two volumes to find the volume of the gap between the vases:
288 π– 162π= 126πin^3. This is the volume of sand needed for
each vase, so multiplying that by 12 we get 126π×12 = 1,512πin^3. - 189 πm^2. Since the base of the cylinder is six meters wide, it has a
radius of three meters. Therefore the dome will extend 3 meters
above the top of the cylindrical base, making height of the
cylindrical base 19 meters. Calculate the volume of a cylinder that
is 19 meters tall with a radius of three meters: V= (π 32 )(19) = 171πm^2.
Next find half of the volume of the sphere-shaped dome on top
that has a radius of 3: ^12 (^43 π 33 ) = 18πm^2. Add these together to find
the total volume: 171πm^2 + 18πm^2 = 189πm^2. - Less than 20 inches.The volume of a single speaker is π(r^2 × 24
inches) = 2,400πcubic inches. Now solve for the radius. r^2 = 100
square inches. r= 10 inches. The width of each speaker is twice
the radius, or 20 inches. Munine’s shelf is less than 20 inches wide. - 27 feet.Half the volume of a sphere is ^12 (^43 πr^3 ), or ^23 πr^3. If
the volume is 13,122πcubic feet, then the radius is 27 feet
(^3 19,683= 27). The height of the dome is equal to the radius
of the dome; therefore the height is also 27 feet.
Set 84
- 4,096πsquare centimeters.Surface area of a whole sphere is
4 πr^2. The surface area of half a sphere is 2πr^2. Each sphere’s
surface area is 2π(8 centimeters^2 ), or 128πsquare centimeters.
Now, multiply the surface area of one half sphere by the 32 halves:
32 × 128 πsquare centimeters = 4,096πsquare centimeters.
501 Geometry Questions