Name: __________________ Class:        Date: _____________
(First Page)
Name: __________________ Class:        Date: _____________
(Subsequent Pages)

There is a rectangular box with the origin and as opposite vertices and with its faces parallel to the coordinate planes. Find the length of the diagonal of the box. Please round the answer to the nearest hundredth.

  ________  

Find the lengths of the sides of the triangle with vertices , , and .

Is it a right triangle?

Is it an isosceles triangle?

Find the distance from to each of the following.

(a) The xy-plane.

  ________  

(b) The yz-plane.

  ________  

(c) The xz-plane.

  ________  

(d) The x-axis. Please round the answer to two decimal places.

  ________  

(e) The y-axis. Please round the answer to two decimal places.

  ________  

(f) The z-axis. Please round the answer to two decimal places.

  ________  

Find an equation of the sphere that passes through the point and has center .

    a.
  
    b.
  
    c.
  
    d.
  
    e.
  

The equation represents a sphere.

Find its center.

Find its radius.

Find equations of the spheres with center that touch

(a) the xy-plane
(b) the yz-plane
(c) the xz-plane

    a. (a)
(b)
(c)
  
    b. (a)
(b)
(c)
  
    c. (a)
(b)
(c)
  
    d. (a)
(b)
(c)
  
    e. (a)
(b)
(c)
  

Find an equation of the largest sphere with center that is contained in the first octant.

Write inequalities to describe the region.

The solid upper hemisphere of the sphere of radius 3 centered at the origin.

    a. ,
  
    b. ,
  
    c. ,
  
    d. ,
  
    e. ,
  

Consider the points P such that the distance from P to is twice the distance from P to . The set of all such points is a sphere.

Find its radius.

Find its center.

Find an equation of the set of all points equidistant from the points and .

    a.
  
    b.
  
    c.
  
    d.
  
    e.
  

PAGE 1 (First Page)
PAGE 1 (Subsequent Pages)
ANSWER KEY

hw13.1 


1 
2 , no, no
3 





4 b
5 ,
6 e
7 
8 b
9 ,
10 c

ANSWER KEY - Page 1