Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Classwork and Homework 39
1. A square pyramid has a slant height of 12 cm and a lateral edge of 15 cm.
a. What is the perimeter of the base?
b. What is pyramid’s lateral area?
c. What is the base area?
d. What is the total area of the pyramid?
2. A regular tetrahedron (“four faces”) is a pyramid with four equilateral triangular faces. If a
regular tetrahedron has an edge of 6 cm, what is its total surface area?
3. Find the total surface area of each solid:
d
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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4. Find the total (including the rectangular face) surface area of a half cylinder with a radius of 5 in
and a height of 2 in.
5. Find the volume of the prism shown.
6. The cylindrical glass is full of water, which is poured into the rectangular pan. Will the pan
overflow? Show work to show the difference in capacity, if one exists.
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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7. Nadia has a box shaped like a right rectangular prism. What is the width of the box?
• The length of the box is 5 feet.
• The height of the box is 2 feet.
• The volume of the box is 30 cubic feet.
Picture:
Equation(s):
Solution (with units):
8. A can of chili and a can of soup are both in the shape of a right circular cylinder.
• The cans are of equal height.
• The radius of the can of chili is 2 times the radius of the can of soup.
The volume of the can of chili is how many times the volume of the can of soup?
Picture:
Solution (with units):
Equation(s):
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Paul designed the original external fuel tank for a spacecraft. The tank is in the shape of a right
circular cylinder. The diagram below shows the tank’s dimensions.
9.
a. What is the radius, in feet, of the tank? Show or explain how you got your
answer.
b. What is the total amount of fuel, in cubic feet, that the tank holds when it is
full? Show or explain how you got your answer.
Patrick is planning the design for a new tank that will also be in the shape of a right circular
cylinder. When the new tank is full, it must hold 2 times the amount of fuel that the original tank
held. Patrick is investigating two design options, which he calls Design P and Design Q.
c. For Design P, the radius of the new tank would be the same as the radius of the original tank.
What should be the height, in feet, of the new tank in Design P? Show or explain how you got your
answer.
d. For Design Q, the height of the new tank would be the same as the height of the original tank.
What should be the radius, in feet, of the new tank in Design Q? Show or explain how you got your
answer.
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
10. A monument in the shape of a right square pyramid is located in a park. The park is in the
shape of a rectangle. The measurements of the monument and the park are shown in the diagram
below.
a. What is the area, in square meters, of the base of the monument? Show or explain how you
got your answer.
b. What is the area, in square meters, of the park, not including the base of the monument?
Show or explain how you got your answer.
c. What is the lateral surface area, in square meters, of the monument? Show or explain how
you got your answer.
The height of the monument is 24 meters.
d. What is the volume, in cubic meters, of the monument? Show or explain how you got your
answer.
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
11. The diagram below shows a right circular cone and its measurements. What is the lateral
surface area of the cone?
Equation:
Solution:
12. A cube has a volume of 27 cubic inches. What is the total surface area of the cube?
Picture:
Solution:
Equation: