APPLICATIONS OF VOLUME FORMULAS

Three tennis balls are sold in a cylindrical container as shown. The cylinder has the same diameter as the tennis balls, 5.4 in. The height of the container is equal to the length of three tennis balls arranged in a line. a. What is the volume of the container?

• $120\pi\ in^3$

• $118.1\pi\ in^3$

• $115\pi\ in^3$

• $130.5\pi\ in^3$

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

hree tennis balls are sold in a cylindrical container as shown. The cylinder has the same diameter as the tennis balls, 5.4 in. The height of the container is equal to the length of three tennis balls arranged in a line. What is the total volume of the three tennis balls?

• $78.8\pi\ in^3$

• $80.5\pi\ in^3$

• $75\pi\ in^3$

• $9.7\pi\ in^3$

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

hree tennis balls are sold in a cylindrical container as shown. The cylinder has the same diameter as the tennis balls, 5.4 in. The height of the container is equal to the length of three tennis balls arranged in a line. What is the volume of the empty space of the cylinder?

• $35.5\pi\ in^3$

• $10\pi\ in^3$

• $45\pi\ in^3$

• $39.3\pi\ in^3$

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A cylindrical container has a height of 9 cm and a cap in the form of a semi-sphere with radius 2 cm. Find The volume of the cylinder without the cap.

• $30\pi\ cm^3$

• $18\pi\ cm^3$

• $36\pi\ cm^3$

• $40.5\pi\ cm^3$

A cylindrical container has a height of 9 cm and a cap in the form of a semi-sphere with radius 2 cm. Find the volume of the semi-spherical cap.

• $5.3\pi\ cm^3$

• $10.6\pi\ cm^3$

• $11\pi\ cm^3$

• $7.5\pi\ cm^3$

A cylindrical container has a height of 9 cm and a cap in the form of a semi-sphere with radius 2 cm. Find the total volume of the shape.

• $40\pi\ cm^3$

• $35.5\pi\ cm^3$

• $41.3\pi\ cm^3$

• $45.5\pi\ cm^3$

If you slice a cone parallel to its base into two parts, you get a smaller cone and a shape called frustum. Find the volume of the frustum created when a cone with a height of 8 in. and a radius of 6 in. is slice of a cone with height of 16 in. and a radius of 12 in.

• $V\ =\ 768\pi\ -\ 96\pi\ =\ 672\pi\ in^3$

• $V\ =\ 700\pi\ -\ 100\pi\ =\ 600\pi\ in^3$

• $V\ =\ 750\pi\ -\ 100\pi\ =\ 650\pi\ in^3$

• $V\ =600\pi\ -\ 90\pi\ =510\pi\ in^3$

I have a cylindrical container with radius 5 cm and a height of 20 cm. I want to put inside of the container some marbles with radius of 1 cm. How many marbles can I put inside of the container?

• 500 marbles

• 1,000 marbles

• 375 marbles

• 425 marbles

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

a bead of a necklace has the radius of 50 mm. The cylindrical hole in the middle has a radius of 1mm and a height of 100 mm. find the volume of the bead of a necklace.

• $V\ =\ 166,666.6\pi\ -\ 100\pi\ =166,566.6\pi\ mm^3$

• $V\ =175,000\pi\ +\ 100\pi\ =175,100\pi\ mm^3$

• $V\ =166,666.6\pi\ +100\pi\ =166,766.6\pi\ mm^3$

• $V\ =\ 5,000\pi\ -\ 100\pi\ =4,900\pi\ mm^3$

Find the volume of a shape with a semi-circle with diameter 18 cm on top of a cone with the same diameter and a height of 26 cm.

• $V\ =972\pi\ +\ 702\pi\ =\ 1,674\pi\ cm^3$

• $V\ =972\pi\ -\ 702\pi\ =270\pi\ cm^3$

• $V\ =702\pi\ -\ 486\pi\ =\ 216\pi\ cm^3$

• $V\ =486\pi\ +\ 702\pi\ =\ 1,188\pi\ cm^3$