Volume of Cones (Grades 11-12)

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Volume of Cones

1. 
The distance around a cone shaped pile of sand containing [math]50265 \ "ft"^3[/math] of sand is [math]251 \ "ft"[/math]. How tall is the sand pile?
  1. [math]12 \ "ft"[/math]
  2. [math]36 \ "ft"[/math]
  3. [math]30 \ "ft"[/math]
  4. [math]43 \ "ft"[/math]
2. 
A sculptor is commissioned to carve a granite block into a cone shape which weighs [math]5000 \ "lb"[/math]. The finished height needs to be [math]5 \ "ft"[/math]. Knowing that granite weighs about [math]165 \ "lb"//"ft"^3[/math], what will be the finished diameter of the sculpture?
  1. [math]4.8 \ "ft"[/math]
  2. [math]2.6 \ "ft"[/math]
  3. [math]13.2 \ "ft"[/math]
  4. [math]2.3 \ "ft"[/math]
3. 
A conical punch bowl has a circumference of 9 ft 6 in and a depth of 2 ft 3 in. How many gallons can the bowl hold? ( [math]7.48 \ "gal"//"ft"^3[/math])
  1. [math]15 \ "gal"[/math]
  2. [math]40 \ "gal"[/math]
  3. [math]5 \ "gal"[/math]
  4. [math]35 \ "gal"[/math]
4. 
The road maintenance crews want to fill the orange traffic cones with sand to make them more stable. The workers use [math]30 \ "ft"^3[/math] of sand to fill [math]100[/math] cones which each have a diameter of 10 inches. How many inches tall are the cones?
  1. [math]13[/math]
  2. [math]22[/math]
  3. [math]20 [/math]
  4. [math]29[/math]
5. 
An ice cream cone 4" high can hold 6 cubic inches of ice cream inside the cone. What is the distance around the top of the cone?
  1. 7.5"
  2. 6"
  3. 13"
  4. 4"
6. 
A granary with a capacity of 2488 cubic feet is shaped like a cylinder with an inverted cone on the bottom. The cylinder is 12 ft across and 20 ft high. How tall is the cone part of the granary?
  1. 13 ft
  2. 14 ft
  3. 3 ft
  4. 6 ft
7. 
A teepee has a volume of [math]3","141 \ "ft"^3[/math]. If the circumference is [math]63 \ "ft"[/math], how tall is the teepee?
  1. 18 ft
  2. 33 ft
  3. 30 ft
  4. 22 ft
8. 
A funnel is [math]12 \ "cm"[/math] tall and can hold [math]200 \ "cm"^3[/math]. What is the diameter of the top of funnel?
  1. 3 cm
  2. 13 cm
  3. 6 cm
  4. 8 cm
9. 
A cone shaped paper cup has a volume of 2 cubic inches and a height of 2 inches. What is its diameter?
  1. 1.5 in
  2. 2 in
  3. 2.75 in
  4. 1.25 in
10. 
A 7 inch tall cup has a diameter of 3.5 inches. Water is poured to a level of 5 inches and then stirred in a circular motion until the water reaches the rim of the glass leaving a cone shaped vortex in the center. How far from the bottom of the glass is the tip of the vortex? (Hint: What is the volume of the vortex?)
  1. 1 in
  2. .75 in
  3. 1.5 in
  4. 2.5 in

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