# 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?

- [math]12 \ "ft"[/math]
- [math]36 \ "ft"[/math]
- [math]30 \ "ft"[/math]
- [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?

- [math]4.8 \ "ft"[/math]
- [math]2.6 \ "ft"[/math]
- [math]13.2 \ "ft"[/math]
- [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])

- [math]15 \ "gal"[/math]
- [math]40 \ "gal"[/math]
- [math]5 \ "gal"[/math]
- [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?

- [math]13[/math]
- [math]22[/math]
- [math]20 [/math]
- [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?

- 7.5 "
- 6 "
- 13 "
- 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?

- 13 ft
- 14 ft
- 3 ft
- 6 ft

7.

A teepee has a volume of [math]3141 \ "ft"^3[/math]. If the circumference is [math]63 \ "ft"[/math], how tall is the teepee?

- 18 ft
- 33 ft
- 30 ft
- 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?

- 3 cm
- 13 cm
- 6 cm
- 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?

- 1.5 in
- 2 in
- 2.75 in
- 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 in
- .75 in
- 1.5 in
- 2.5 in

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