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

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

What this topic is

Surface area measures the outside of a solid in square units, while volume measures the space inside in cubic units, and Solid geometry (surface area, volume) checks both.

For a rectangular box, surface area adds the areas of three pairs of matching faces. Formulas for spheres, cones and cylinders are usually given in the question, so the work is substituting and solving, often backward from a known volume or area to find a radius.

A frequent slip is forgetting to take a square root after solving for r squared. Answer choices also tempt with the result of counting only three faces of a box instead of all six.

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, in square centimeters, of the box?

74✗ Not this one120✗ Not this one148✓ Correct240✗ Not this one

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Answer: C — 148

Surface area is $2 (6 \cdot 5 + 6 \cdot 4 + 5 \cdot 4) = 2 (30 + 24 + 20) = 148$ . Omitting the factor of 2 or computing volume $6 \cdot 5 \cdot 4 = 120$ yields common distractors.

Question 2Mid

A spherical ornament has surface area $100 π$ square centimeters. What is the radius, in centimeters, of the ornament? (Use $S A = 4 π r^{2}$ .)

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

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Answer: B — 5

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

Question 3Mid

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

(V = \frac{1}{3} π r^{2} h)

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

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Answer: D — 4 cm

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

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

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