Volume of a Cylinder | Mensuration | Assessment | English | Grade 8

Volume of a cylinder with radius r and height h is equal to _________.

• πr³h

• 2πr²h

• πr²h

• πr²h/2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The volume of a cylinder whose radius is 9 cm and height is 21 cm is equal to ______.

• 10692 cm³

• 5346 cm³

• 48114 cm³

• 2673 cm³

Answer explanation

Volume of cylinder = πr²h = (22/7) × 9 × 9 × 21 = 5346 cm³ So, Option 2 is correct.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The volume of a cylinder is 44352 m³. If the radius of the cylinder is 21 m, what is the height of the cylinder?

• 37 m

• 35 m

• 39 m

• 32 m

Answer explanation

Volume of a cylinder = πr²h According to the question, we have, 44352 m³ = (22/7) × 21 m × 21 m × h 44352 m³ = 1386 ² × h i.e., h = 44352 m³/ 1386 m² = 32 m So, option 4 is correct.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If the height of a cylinder becomes 1/9 of the original height and the radius is tripled, then which of the following will be true?

• Volume of the cylinder will be tripled

• Volume of the cylinder will remain unchanged.

• Volume of the cylinder will be halved.

• Volume of the cylinder will be 1/9 of the original volume.

Answer explanation

Let the radius be r and height be h of a cylinder Volume of the cylinder = πr²h .....(1) Now, assume that the height of the cylinder becomes 1/9 of the original height and the radius is tripled, i.e., h' = h/9 and r' = 3r So, volume of the new cylinder = π(r')² h' = π(3r)² (h/9) = 9 πr²h/9 = πr²h ......(2) From (1) and (2), we can see that the volume remains unchanged. So, option 2 is correct.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Volume of a cylindrical container is 44000 m³. If the height of the container is 35 m, what is its radius?

• 26 m

• 23 m

• 20 m

• 29 m

Answer explanation

Volume of cylinder = πr²h According to the question, we have, 44000 = (22/7) × r² × 35 44000 = 110 × r² r² = 44000/110 = 400 i.e., r = 20 m So, option 3 is correct.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A cylindrical drum of diameter 36 m and height 126 m is filled with cubes of side 4 m each. Approximately how many such cubes will be required?

• 2005

• 2004

• 2007

• 2010

Answer explanation

Volume of a cube = l³ = 4³ = 64 m³ diameter = 36 m So, radius = r = 36/2 = 18 m Volume of cylinder = πr²h = (22/7) × 18² × 126 = 128304 m³ Number of cubes that are required = volume of cylinder/ Volume of a cube = 128304 m³ / 64 m³ = 2004.75 So, approximately 2004 cubes are required. So, option 2 is correct.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3