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?
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?
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