Geometry CC
1.
Assignment #53
Volume of a Cone
The right circular cone shown below has a base with radius of 7.
The slant height of the cone’s lateral surface is
Find the exact value of the volume of the cone.
130 .
2.
A cone with diameter 15 cm and a height of 4 cm.
Find the exact value of the volume.
3.
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
cup, how high will the water reach in the cylindrical cup?
4.
In the diagram below, a right circular cone with a radius of 3 inches has a slant height of
5 inches. There is a right cylinder with a radius of 4 inches and a height of 6 inches.
Determine and state the number of full cones of water needed to completely fill the
cylinder with water.
R1. MNO  PQR . Which of the following statements is not necessarily true?
[Diagram must be shown for your answer – not just an answer choice.]
(1) NO  QR
(2) QP  NM
(3) OMN  RQP
(4) NOM  QRP
R2. At a local pizza parlor, the large pies have a diameter of 16 inches. Each large pie can
be cut into either 8 or 12 uniform slices based on customer preference. How much
larger is the area of a slice of pizza from the 8-piece pie than the area of a slice of pizza
from the 12-slice pie? Round your answer to the nearest tenth of a square inch.
R3. Which equation represents the line perpendicular to y = x – 2 that passes through the
point (2, – 1)? [Work must be shown – not just an answer written.]
(1) y 
1
x 1
2
(2) y  x  1
(3) y   2x  1
R4. If cos  3n  7   sin 5n  3 , what is the value of n?
1.
2.
3.
4.
147
75
2 inches
8
R1.
R2.
R3.
R4.
3
8.4 in2
2
23
(4) y  2x  1