SAT Math : Spheres

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #812 : Geometry

 is a point on a sphere, and  is the point on the sphere farthest from . The shortest curve from  to  that is completely on the sphere is  in length. 

Give the volume of the sphere.

Possible Answers:

Correct answer:

Explanation:

The figure referenced is below.  is the center of the sphere.

Sphere

The shortest curve connecting  to its opposite point  is a semicircle. Also,  is a diameter of the sphere, and  and  are radii. 

Given radius , a semicircle has length

Setting  and solving for :

.

The volume of a sphere, given its radius , is

.

Setting :

 

Example Question #41 : Spheres

Find the volume of a sphere whose diameter is 10cm.

Possible Answers:

Correct answer:

Explanation:

Radius is half of the diameter. Half of 10cm is 5cm.

Example Question #43 : Spheres

Spheres  element76

The radius of the sphere shown here is  long. What is its volume?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume  of a sphere given its radius  is

The radius is stated to be  long; hence, we can calculate the sphere's volume by substituting this value for  into the formula, as shown:

Hence, the volume of the sphere is 

 

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