Solid geometry (surface area, volume) — ISEE Upper practice questions

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95 practice questions in the app
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Practice 95 Solid geometry (surface area, volume) questions in the app

What this topic is

Solid geometry (surface area, volume) on the ISEE Upper Mathematics Achievement test covers finding the surface area and volume of three-dimensional figures such as rectangular boxes, spheres, and cones.

A student must choose the correct formula, substitute given dimensions, and solve for a missing measure such as a radius when area or volume is known. Items usually appear as short word problems about everyday objects, and the needed formula is sometimes printed in the stem.

Answer choices are typically lengths, areas, or volumes, often written with π. Common traps include mixing surface area with volume, omitting a face of a closed solid, or treating a diameter as a radius.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

A closed rectangular box measures 6 cm by 5 cm by 4 cm. What is the total surface area of the box?

74\text{ cm}^2

✗ Not this one

120\text{ cm}^2

✗ Not this one

148\text{ cm}^2

✓ Correct

240\text{ cm}^2

✗ Not this one

Show answer

Answer: C — $148\text{ cm}^2$

Surface area is $2(6\cdot5 + 6\cdot4 + 5\cdot4) = 2(30 + 24 + 20) = 148$ . Omitting the factor of 2 or computing volume $6\cdot5\cdot4 = 120$ yields common distractors.

Question 2Mid

A spherical ornament has surface area $100\pi$ square centimeters. What is the radius of the ornament?

(SA=4\pi r^{2})

10 cm✗ Not this one5 cm✓ Correct25 cm✗ Not this one50 cm✗ Not this one

Show answer

Answer: B — 5 cm

$4\pi r^{2}=100\pi$ ⇒ $r^{2}=25$ ⇒ $r=5$ .

Question 3Mid

An ice-cream cone has volume $48\pi$ cubic centimeters and height 9 centimeters. What is the radius of its circular base?

(V=\dfrac{1}{3}\pi r^{2}h)

8 cm✗ Not this one6 cm✗ Not this one12 cm✗ Not this one4 cm✓ Correct

Show answer

Answer: D — 4 cm

$48\pi=\dfrac{1}{3}\pi r^{2}(9)$ ⇒ $48=3r^{2}$ ⇒ $r^{2}=16$ ⇒ $r=4$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 95 Solid geometry (surface area, volume) questions in the app

Solid geometry (surface area, volume) — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement