Hwk. #8
Name ______________________
CCGeometry 10X
Date_________
1. What is the volume formula for a right circular cone with radius r and height h?
2
V = 1/3Bh or 1/3πr h
right triangular pyramid 2. Classify the solid shown: ________
___________ _________
Find its volume.
V = 1/3Bh
= 1/3(½)(2√5)(3)(4)
4
6
3
= 4√5 units2
3. Find the volume of the right rectangular pyramid shown.
V = 1/3Bh
= 1/3(144)(16)
= 768 units3
16
12
12
4. Find the volume of the circular cone below. Round your answer to the nearest
hundredth.
V = 1/3Bh
= 1/3(π)(14)2(27)
≈ 5541.77 units3
27
14
5. Find the volume of a pyramid whose base is a square with edge length 3 andwhose
height is also 3.
V = 1/3Bh
= 1/3(9)(3)
= 9 units3
6. Suppose you fill a conical paper cup with a height of 6‛‛ with water. If all the
water is then poured into a cylindrical cup with the same radius and same height as
the conical paper cup, to what height will the water reach in the cylindrical cup? 1/3πr2(6) = πr2h
h = 2 in.
7. Sand falls from a conveyor belt and forms a conical pile on a flat surface. The
diameter of the pile is approximately 10 ft. and the height is approximately 6 ft.
Estimate the volume of the pile of sand to the nearest cubic foot.
V =1/3πr2h
= 1/3π(5)2(6) = 50
≈ 157 ft3
8. Use the diagram to the right to answer the questions that follow.
a. Determine the volume of the cone shown. Give an exact answer.
V =1/3πr2h
= 1/3π(16)(11)
= 176π units3
3
b. Would a cone with height 33 and radius 12 be a similar cone?
11 = 33
Show work to justify your answer.
4 12
11 = 11
4 4
yes
c. Calculate the volume of the cone described in part (b).
V =1/3π(144)(33)
= 1584π units3
9. Review: In right ΔABC below, CD is the altitude to hypotenuse AB, CB = 6, and
AD = 5. Find BD.
x = _x_
S M L
L1 x 6
L2 5
H 6 x+5
4 x+5
x2 + 5x ­ 36 = 0
(x + 9)(x ­ 4) = 0
x = ­9 / x = 4
CC Geometry X
Aim 9: How do we compute the volume and surface area of a sphere?
Do Now:
1. Complete: A circle with center C and radius r is the set of all points in a plane a
given distance r, called the ______________, from a given point C, called the
_______________.
2. Picture a marble and a beach ball. Which one would you describe as a sphere?
___________What is a significant difference between the two figures?
Definition: Given a point C in three-dimensional space and a number r > 0, the sphere
with center C and radius r is the set of all points in space that are a distance r from
Examples of spheres: beach ball, soap bubble
the point C.
Definition: Given a point C in three-dimensional space and a number r > 0, the solid
sphere (or ball) with center C and radius r is the set of all points in space whose
distance from the point C is less than or equal to r.
Examples of solid spheres include: marble, planet
A sphere is _________________ while a solid sphere is _________________
The term hemisphere refers to a half-sphere, and solid hemisphere refers to a
solid half-sphere.
Formula for Volume of a Sphere
Formula for Surface Area of a Sphere
SA = 4πr
where r = length of the radius
Examples:
1) Write a formula for the volume of the hemisphere.
2
2) Find the surface area and volume of a sphere with a diameter of 12 cm. (Round
to tenths place.)
2
3) Find, in terms of π, the volume of a sphere whose surface area is 256π cm .
3
4) Find, in terms of π, the surface area of a sphere whose volume is 4500π cm .
5) Find, to the nearest tenth, the surface area of a sphere whose volume is
3
18.432π cm .
6) Snow globes consist of a glass sphere that is filled with liquid and other
contents. If the inside radius of the snow globe is 3 inches, find the
approximate volume of material, to the nearest cubic inch, that can fit
inside.
7) An ice cream cone is 12 cm deep and 5 cm across the opening in the cone. A
sphere-shaped scoop of ice cream with a diameter of 5 cm is placed in the cone.
If the ice cream melts completely into the cone, will the cone overflow?
8) In a can of tennis balls that is exactly three balls high, which is greater,
the volume of the balls, or the volume of the air around the balls?
(Disregard the thickness of the balls.)
9) Bouncy rubber balls are composed of a hollow rubber shell 0.4 inches thick and
an outside diameter of 3.2 inches. The price of the rubber needed to produce this
3
toy is $0.035/in .
a) What is the cost of producing one case, which holds 50 rubber balls? Round to
the nearest cent.
0.4
3.2
b) If each ball is sold for $0.40, how much profit is earned on each ball sold?
Let's Sum it Up!
Volume of a Sphere:
Surface Area of a Sphere:
Hwk. # 9
Name_______________________
CC Geometry 10X Date __________
1) A solid sphere has volume 36π. What is the radius?
2) A sphere has surface area 16π. What is the radius?
3) Find, to the nearest tenth, the surface area of a sphere whose volume is
3
62.208π cm .
4) The radii of two spheres are 5 and 8. What is the ratio of the
surface areas? __________ the volumes? _________
5) A right circular cone has radius 5 cm and slant height 13 cm. Find the volume,
in terms of π.
Review
1) The radius of each circle is 1 cm. The hypotenuse of the
isosceles right triangle measure
cm. Find the area
inside the triangle, but outside the circles, to the nearest
hundredth cm. 2) A cone and a cylinder have the same radius and height. What is the ratio of
the volume of the cone to the volume of the cylinder?
(a) 1:2
(b) 1:3
(c) 1: π
(d) 1:1
3
3
3) The volumes of two similar cylinders are 512 cm and 2197 cm . What is
the ratio of their heights? __________ their lateral areas? __________
4) Which figure has the greatest area?
60
0
15 m
26
5) Find the volume of the cone in terms of π.
26 in.
20 in