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Algebra & Analytic Geometry
3D Solids
Name & Date
REVIEW
Directions: Find the lateral area, surface area and volume of each figure.
1)
Lateral Area
Surface Area
Volume
2)
Lateral Area
Surface Area
Volume
3)
Lateral Area
Surface Area
Volume
4)
Lateral Area
Surface Area
Volume
5) The regular pentagonal prism and regular pentagonal pyramid below both have a base edge of length 20in and a
height of 36in.
A) Find the area of each base.
B) Find the volume of each solid.
C) Find the surface area of the prism.
D) Find the slant height of the pyramid and its total surface area.
Algebra & Analytic Geometry
3D Solids
Name & Date
REVIEW
6) The volume of the regular hexagonal pyramid to the right is 432 3 cm 3 and has a base perimeter of 72 cm.
Leave all answers in exact form.
A) Find the area of the base.
B) Find the height of the pyramid.
C) Find the slant height of the pyramid.
D) Find the surface area of the pyramid.
7) The great circle of a sphere has circumference 18π inches. Find its EXACT volume and EXACT surface area.
8) The volume of a sphere is 36π in3. Find the EXACT surface area.
9) A cylinder with a 10-foot radius has a total surface area of 1413.7 square feet. What is the height of the
cylinder to the nearest tenth?
10) The surface area of a cone is 75 ft2. If the radius of the base is 5 ft, find the volume of the cone.
11) Calculate the surface area of a hemisphere with volume 18π ft3. Calculate its surface area. (Remember this
is not as simple as dividing surface area of a sphere by 2)
12) A garbage can is in the shape of a hemisphere on top of a cylinder. If the base of the garbage can has
circumference 30π inches and the height of the cylinder part is 40 inches, what is the volume of the can?
Algebra & Analytic Geometry
3D Solids
Name & Date
REVIEW
13) The prism below has a regular hexagonal base with a perimeter of 84in and a volume of 7056 3 in 3 .
A) Find the exact area of the base.
B) Find the height of the solid.
C) Find the total surface area.
14) Find the surface area and volume of the sphere.
Surface Area
Volume
15) The volume of a sphere is 36π in3. Find the EXACT surface area.
16) A solid is composed of a cone on top of a cylinder. If the base of the cone has circumference 10π meters and
the height of both parts is twice the radius, find the volume of the composite solid. Round to the nearest tenth.
17) The surface area of a cone is 328.8 square inches. If the diameter of the cone is 13 inches, find its volume.
Round to the nearest tenth.