Applying Volume of Spheres Warmup

What is the formula(s) to solve for volume of a sphere?

Answer explanation

The formula for the volume of a sphere is (4/3)πr^3 or 4πr^3/3.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Find the volume of the hemisphere

• 134.0 m³

• 100.5 m³

• 267.9 m³

• 201.6 m³

Answer explanation

The volume of a hemisphere is calculated using the formula V = (2/3) * π * r^3. Given the radius, the volume is 134.0 m^3.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Kayla has two spherical gazing balls in her yard.

(see picture). Which statement about their volumes is true?

• The volume of Ball 2 is twice the volume of Ball 1.

• The volume of Ball 1 is 8 times the volume of Ball 2.

• The volume of Ball 1 is twice the volume of Ball 2.

• The volume of Ball 2 is 8 times the volume of Ball 1.

Answer explanation

The correct statement is that the volume of Ball 1 is 8 times the volume of Ball 2, as the volume of a sphere is proportional to the cube of its radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Barney wanted to know how much ice cream he got in one scoop. The radius of a scoop is 2 inches. Find the volume. Use 3.14 for pi.

• 345.3 in³

• 33.5 in³

• 25.1 in³

• 50.2 in³

Answer explanation

The volume of a sphere is calculated using the formula V = (4/3) * π * r^3. Substituting the radius (2 inches) into the formula gives V = (4/3) * 3.14 * 2^3 = 33.5 in³, which is the correct answer choice.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Jack wants to know how much water a sphere can hold with a radius of 8 cm. Find the volume. Use 3.14 for pi.

• 83.6 cm³

• 2144.7 cm³

• 254 cm³

• 2220 cm³

Answer explanation

The volume of a sphere is calculated using the formula V = (4/3) * π * r^3. Substituting the values, V = (4/3) * 3.14 * 8^3 = 2144.7 cm³. Therefore, the correct answer is 2144.7 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Fill in the blank with the correct letters. Letter ___ represents the diameter. Letter ___ represents the radius.

___, ___

(a)  

Which statements are true? Check all that apply.

• The height of the cylinder is equal to the diameter of the sphere.

• The height of the cylinder is two times the diameter of the sphere.

• The radius of the sphere is half the height of the cylinder.

• The diameter of the sphere is equal to the radius of the cylinder.

• The volume of the sphere is two-thirds the volume of the cylinder.

Answer explanation

The correct statements are: The height of the cylinder is equal to the diameter of the sphere, the radius of the sphere is half the height of the cylinder, and the volume of the sphere is two-thirds the volume of the cylinder.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3