Common Core Standard HSG-GMD.A.3 Questions

Grade 11 Volume CCSS: HSG-SRT.C.8, HSG-GMD.A.3

A cube with a volume of [math]27 \ "m"^3[/math] is inscribed inside a sphere. What is the volume of the sphere?

[math](9 pi)/(2) \ "m"^3[/math]
[math]9 sqrt(2) pi \ "m"^3[/math]
[math](27sqrt(3)pi)/2 \ "m"^3[/math]
[math]108sqrt(3) pi \ "m"^3[/math]

Grade 11 Volume CCSS: HSG-GMD.A.3, HSG-MG.A.2

Several maple trees were recently cut. The felled logs were approximately cylinders, 1.5 m in diameter and 6 m long. They were milled on-site into boards. During the milling process, about 15% of the volume of wood from the tree is lost. The density of the wood is [math]673 \ "kg"//"m"^3[/math]. If 16 maple trees were initially cut down, and the trucks that transport the boards can carry up to 18,143 kg, how many truck loads will be required to transport all the boards?

Grade 9 Volume CCSS: HSG-GMD.A.3

What is the maximum volume of a sphere that would fit into the cube if the measurement of AD is 12 mm.

Explain your answer.

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3

A cylindrical cup has a height of 15 cm and width of 8 cm. It is completely full of water. A ball, with a diameter of 8 cm, is placed into the cup of water, causing some of the water to spill over the edge of the cup. The ball only fits halfway (half of the ball is still above the top of the glass). Once the ball is taken out of the cup, what is the height of the remaining water in the cup? Round the answer to one decimal place.

Grade 11 Volume CCSS: HSG-GMD.A.3, HSG-MG.A.2

Sarah and Tim are getting married, and their wedding rings will both made of platinum. The rings are both shaped like a hollow cylinder, both having a width of 3 mm and a thickness of 1.5 mm (the thickness is the difference between the inner diameter and the outer diameter). The inner diameter of Sarah's ring is 16 mm, and the inner diameter of Tim's ring is 17.5 mm. If the density of platinum is [math]21.45 \ "g"//"cm"^3[/math], and the cost of platinum is about $36.33 per gram, what is the cost (for materials) of the two rings?

$293.32
$402.11
$870.33
$1,434.38

Grade 10 Three Dimensional Shapes CCSS: HSG-GMD.A.3

What is the height of a cylindrical tank that holds about 203,374 cubic feet of material in it? The diameter of the tank is 34 feet.

Grade 10 Volume CCSS: HSG-GMD.A.3

Find the volume of a square pyramid with a base of 10 inches wide and a height of 18 inches.

180 cubic inches
360 cubic inches
1800 cubic inches
600 cubic inches

Grade 11 Volume CCSS: HSG-GMD.A.3, HSG-MG.A.1

A backyard pool is shaped like a cylinder. If the water in the pool is 6 ft deep, and the pool has a diameter of 15 ft, water is the volume of water in the pool, rounded to the nearest cubic foot?

[math]338 \ "ft"^3[/math]
[math]1","060 \ "ft"^3[/math]
[math]1","696 \ "ft"^3[/math]
[math]4","241 \ "ft"^3[/math]

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3, HSG-MG.A.2

A cylindrical object has a diameter of 10 mm and a length of 40 mm. It has a density of [math]0.51 \ "g"//"mm"^3[/math]. What is the mass of the object, rounded to one decimal place?

0.3 g
20.4 g
40.0 g
1602.2 g

Grade 11 Volume CCSS: HSG-GMD.A.3, HSG-MG.A.1

A certain perfume bottle is shaped like a right rectangular pyramid. If the dimensions of the base are 5 cm by 8 cm, and it is 25 cm tall, what is the volume of perfume in the bottle, if it is full, to the nearest milliliter? Hint: [math]1 \ "ml" = 1 \ "cm"^3[/math].

333 ml
500 ml
1,000 ml
1,047 ml

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3, HSG-MG.A.3

A company that produces hollow rubber balls wants to design a new, larger ball. It has found that the thickness of the rubber (which is constant) has to be at least a fifth the size of the radius of the ball. What is the least amount of rubber that each ball will need if the new ball being designed is 15 cm in diameter? Round the answer to one decimal place.

[math]862.4 \ "cm"^3[/math]
[math]904.8 \ "cm"^3[/math]
[math]1385.4 \ "cm"^3[/math]
[math]1767.1 \ "cm"^3[/math]

Grade 11 Volume CCSS: HSG-GMD.A.3, HSG-MG.A.1

A city is storing salt to use during the winter on its roads. The salt is stored in piles that resemble a cone. The piles are 7 m high and have a diameter of 19 m. What is the volume of salt in each pile, rounded to the nearest cubic meter?

[math]70 \ "m"^3[/math]
[math]211 \ "m"^3[/math]
[math]331 \ "m"^3[/math]
[math]662 \ "m"^3[/math]

Grade 11 Three Dimensional Shapes CCSS: HSG-SRT.C.8, HSG-GMD.A.3, HSG-MG.A.3

A pile of sand is in the shape of a cone. The pile is 5 yd wide. The sand pile cannot be too steep, or the sand will likely spill. Let the angle of elevation of the sides of the pile of sand be [math]theta[/math], as measured between the diameter of the face of the circular part of the cone to the slant height. If the maximum value [math]theta[/math] can be is 60°, what is the maximum volume of sand in the pile, rounded to the nearest cubic yard?

[math]11 \ "yd"^3[/math]
[math]16 \ "yd"^3[/math]
[math]28 \ "yd"^3[/math]
[math]113 \ "yd"^3[/math]

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3, HSG-MG.A.1

A certain type of yarn has a diameter of 4 mm. If there is a ball of yarn (one continuous piece) that is 15 cm in diameter, about how long is the piece of yarn? Round the answer to the nearest meter.

35 m
141 m
422 m
1,125 m

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3, HSG-MG.A.3

Mark is serving drinks at a party. The glasses are in the shape of an inverted cone (with a stem and base, but these parts don't hold any liquid). The conical part of the glass is 3.5 in. wide and 4 in. tall. Because Mark is afraid of spilling, he only ever fills the cup partway. If he only fills each cup to a maximum of 80% of its total height (measured vertically), what is the maximum volume of liquid each cup will hold, as a percent of its total capacity? Round the answer to the nearest tenth of a percent.

16.3%
17.1%
21.1%
51.2%

Grade 11 Volume CCSS: HSG-GMD.A.3

A piece of steel measures 15 cm by 15 cm by 6 cm thick, but two of the rectangular sides (opposite each other) are concave, as if half cylinders were carved out (with height 15 cm and radius 3 cm). What is its volume?

[math]926 \ "cm"^3[/math]
[math]1138 \ "cm"^3[/math]
[math]1350 \ "cm"^3[/math]
[math]1774 \ "cm"^3[/math]

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3, HSG-MG.A.1

A company manufactures solid rubber balls. They package them in a cylindrical container that fits three balls. Once the three balls are in the container, and the container is sitting upright (on one of its circular ends), there is exactly 0.3 in. of space between the top of the highest ball and the top of the container. If the container is 13 inches high, what is the volume of rubber in each ball, rounded to the nearest tenth of a cubic inch?

[math]29.7 \ "in."^3[/math]
[math]39.7 \ "in."^3[/math]
[math]317.0 \ "in."^3[/math]
[math]8","580.2 \ "in."^3[/math]

Grade 11 Three Dimensional Shapes CCSS: HSG-GMD.A.3, HSG-MG.A.3

Given a piece of paper that is 8.5 by 9.5 inches, what is the largest cylinder (in terms of volume) that can be made? The cylinder must have closed ends (two full circles must be cut from the sheet of paper), and the side of the cylinder must be solid (the circles cannot be cut from paper that will be used for the cylinder's side). Assume that the sides of the rectangle which is cut from the piece of paper (to form the side of the cylinder) are parallel/perpendicular/coincident to the sides of the piece of paper. Round the answer to the nearest tenth of a cubic inch.

[math]31.4 \ "in."^3[/math]
[math]35.1 \ "in."^3[/math]
[math]37.2 \ "in."^3[/math]
[math]39.3 \ "in."^3[/math]

Grade 11 Volume CCSS: HSG-GMD.A.3

A cylindrical pill with semispherical ends has a diameter of .5 cm and a total length 1.25 cm. What is the volume of the pill?

[math]0.082 \ "cm"^3[/math]
[math]2.13 \ "cm"^3[/math]
[math]0.213 \ "cm"^3[/math]
[math]0.817 \ "cm"^3[/math]

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Common Core Standard HSG-GMD.A.3 Questions

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