ACT 3D Surface Area — Tutor Intake Assessment
This is a spot-check intake on surface area of prisms, cylinders, pyramids, cones, and spheres. The goal is to find where your understanding breaks down so we can plan instruction — not to grade you. Work as you would on the ACT (no formula sheet). If you don't see how to start a problem, move on and we'll discuss it together.
Concepts
A cylindrical metal can has an open top (no lid) but a closed
bottom. Which expression gives the total area of metal used to
make the can, where r is the radius and h is the height?
When computing total surface area, the lateral surface area is
added to the area of the shape's base(s). Which of the following
correctly pairs a solid with the number of base areas added?
What is the surface area of a sphere of radius r?
Procedures
A closed rectangular box has dimensions 8 cm by 5 cm by 3 cm.
What is its total surface area, in cm^2?
A cylinder has radius 4 cm and height 10 cm. What is its
LATERAL surface area, in cm^2, in terms of pi?
A regular square pyramid has a base edge of 6 m and a slant
height of 5 m. What is its total surface area, in m^2?
A cone has a radius of 5 cm and a (perpendicular) height of
12 cm. What is its LATERAL surface area, in cm^2, in terms
of pi?
A sphere has a diameter of 12 cm. What is its surface area,
in cm^2, in terms of pi?
Applications
A rectangular paper label is wrapped around the side of a
cylindrical can (covering the curved surface only, with no
overlap and nothing on the top or bottom). The can has a
diameter of 10 cm and a height of 10 cm. What is the area
of the label, in cm^2?
A solid cone has a radius of 8 cm and a (perpendicular) height
of 15 cm. What is its TOTAL surface area, in cm^2, in terms
of pi?