Vocab
A solid formed by polygons that enclose a single region of space is called a ________
Polyhedron
What is the equation for the volume of a triangular prism? (include explicit area formula)
V = (1/2bh)H
What is the equation for the area of a circle?
A=πr2
What is the equation for the volume of a rectangular pyramid? (include explicit area formula)
V = 1/3(bh)H
What is the equation for the volume of a cone? (include explicit area formula)
V = 1/3 (πr2)H
The flat polygonal surfaces of a polyhedron are called its ____________
Faces
Find the volume of a rectangular prism that has a height of 45 cm. The two rectangular bases measure 7 cm and 12 cm.
3780 cm3
Find the volume of a cylinder that has a radius of 3 mm and a height of 5 mm. (round to the nearest hundredth)
141.37 mm
Find the volume of the square pyramid with a side length of 5 cm and height of 8 cm. Round to the nearest hundredth.
66.67 cm3
Find the volume of the cone with a radius of 5 cm and height of 10 cm. Round to the nearest hundredth.
261.80 cm
The point of intersection of three or more edges is called a ______________ of the polyhedron
Vertex
Find the volume of a square prism that has a height of 2 feet. The bases of the prism have edges of 9 inches by 9 inches.
1944 in3
Find the volume of a cylinder that has a diameter of 10 m and a height of 12 m. (round to the nearest hundredth)
942.48 m
Find the volume of the rectangular pyramid with side lengths of 7 m, 15 m, and height of 12.5 m.
437.5 m3
Find the volume of the semicircular cone with a diameter of 12 m and height of 14 m. Round to the nearest hundredth.
263.89 m
How many faces does a heptahedron have?
7
Find the volume of a right trapezoidal prism that has a height of 20 cm. The two bases of the trapezoid measure 3 cm and 6 cm, and its height is 4 cm.
360 cm3
Find the radius of a cylinder that has a volume of 6927.21 in and a height of 45 in.
7 in
Find the volume of the trapezoidal pyramid with base lengths of 4 cm and 8 cm, trapezoidal height of 5 cm, and overall height of 15 cm.
150 cm
Use algebra to express the volume of the cone with a radius of b and height of 2b.
V = (2/3)πb2
Both a prism and a cylinder have two bases that are both _________________ and _________________.
Congruent and parallel
If an average rectangular block of limestone used to build the Great Pyramid of Khufu at Giza is approximately 2.5 feet by 3 feet by 4 feet and limestone weighs approximately 170 pounds per cubic foot, what is the weight of one of the nearly 2,300,000 limestone blocks used to build the pyramid?
5100 pounds
Use algebra to express the volume of the right cylinder with a base circumference of pπ and a height of h.
V=(pπ)h
An equilateral triangular pyramid has a volume of 180 cm3 and an overall height of 12 cm. Find the length of a side of the base. (round to the nearest hundredth)
9.49 cm.
A cone has a volume 320 cm3 and a height 16 cm. Find the radius of the base. Round your answer to the nearest 0.1 cm.
4.4 cm