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Solved volume and surface area MCQs — 48 questions on cubes, cylinders and cones: volumes, curved and total surface areas, hollow pipes and rollers, wire drawing, melting coins and cone-in-cube problems, with verified answers and explanations. Free online practice for FPSC, PPSC, NTS and all one-paper exams. Covers volume and surface area.
Paper Snapshot
Questions
48
Time
48
Minutes
Subjects
1
Topics
3
Read mode shows correct answers. Attempt mode hides answers, starts timer, and shows your result after submission.
About this paper
This is the Arithmetic: Volume and Surface Area solved MCQ bank from Advanced FPSC & Other Federal Model Papers (Edition 32): 48 published questions (book pp. 770-773, of 50 printed) on cube, cylinder and cone volumes and surface areas, including hollow pipes and rollers, wire drawing, melting coins into cylinders, conical tents and the largest cone cut from a cube. Every answer was re-solved from scratch and checked against the book's printed Answer Key on p. 773; 24 key errors were corrected to the standard answer, two items were dropped because they cannot be solved as printed, and the remaining print defects were retained at the key and flagged.
Paper Controls
Subject 1
Topic Section
5 solved MCQs shown directly below
Correct Answer: 3 : 1
The edge ratio is the cube root of the volume ratio, cube root of 27 : 1 = 3 : 1.
Correct Answer: 4 : 9
The edges are in the ratio 2 : 3, so the surface areas are in the ratio 2 squared : 3 squared = 4 : 9.
Correct Answer: 1 : 9
The edges are in the ratio 1 : 3, so the face areas are in the ratio 1 squared : 3 squared = 1 : 9.
Correct Answer: becomes 8 times
Volume scales with the cube of the edge, so doubling the edge multiplies the volume by 2 cubed = 8.
Correct Answer: 56.25%
The surface area scales with the square of the edge, so 1.25 squared = 1.5625, an increase of 56.25%.
Topic Section
23 solved MCQs shown directly below
Correct Answer: 44 m3
The radius is 1 m, so the volume is pi x 1 squared x 14 = 44 m3 (the book prints m2 in the options; the unit should be m3).
Correct Answer: None of these
The volume is 0.2464 m3, so pi x r squared x 4 = 0.2464 gives r = 0.14 m and diameter 0.28 m, which is not among the offered values — hence None of these. The printed key letter "e" does not exist among the four options.
Correct Answer: 13860 cm3
From 2 pi r = 66, r = 10.5 cm, and from 2 pi r h = 2640, h = 40 cm, so the volume is pi x 10.5 squared x 40 = 13860 cm3.
Correct Answer: 4 : 3
Total surface area over lateral surface area = (r + h) over h = 80 over 60 = 4 : 3.
Correct Answer: 192 cm3
The square tin holds 8 x 8 x 14 = 896 cm3 and the circular tin holds pi x 4 squared x 14 = 704 cm3, so the difference is 192 cm3.
Correct Answer: 3080 cm2
With r = 2x and h = 3x, pi x 4x squared x 3x = 12936 gives x = 7, so r = 14 cm and h = 21 cm, and the total surface area is 2 pi x 14 x 35 = 3080 cm2.
Correct Answer: 1.5
For an open cylinder the interior area is the curved surface plus one base, 5 pi r squared = 616, so r squared = 39.2 and h = 2r; the volume is pi x 39.2 x 2r, about 1540 cm3, about 1.5 litres.
Correct Answer: 4620 m3
From 2 pi r (r + h) = 1628 with r + h = 37, r = 7 m and h = 30 m, so the volume is pi x 49 x 30 = 4620 m3.
Correct Answer: 7 : 3
Radius = 2 x volume over curved surface area = 1848 over 264 = 7 m, so the diameter is 14 m, and the height is 264 over (2 pi x 7) = 6 m, giving 14 : 6 = 7 : 3.
Correct Answer: equal to its diameter
For a given volume the surface area is minimised when the height equals the diameter.
Correct Answer: 1 : 4
Volume scales with the square of the radius, so halving the radius quarters the volume, a ratio of 1 : 4.
Correct Answer: 20 : 27
Volume ratio = (2 squared x 5) : (3 squared x 3) = 20 : 27.
Correct Answer: sqrt 2 : 1
With equal volumes, radius squared is inversely proportional to height, so the radius ratio is sqrt 2 : 1.
Correct Answer: half the volume of Y
Halving the diameter quarters the volume and doubling the height doubles it again, so the new volume is one quarter times 2 = half the volume of Y.
Correct Answer: 9 times
With volume fixed, length is inversely proportional to radius squared, so radius over 3 gives length times 9.
Correct Answer: 2310
The half-full cross-section is half of pi x 3.5 squared = 19.25 cm2, and at 200 cm per second for 600 seconds that discharges 19.25 x 200 x 600 = 2310000 cm3 = 2310 litres. The keyed 4620 litres is the full-pipe figure.
Correct Answer: 640
The cylinder volume is pi x 9 x 8 = 72 pi and each coin is pi x 0.5625 x 0.2 = 0.1125 pi, so 72 over 0.1125 = 640 coins.
Correct Answer: 25 cm
The total volume is pi x (225 x 35 + 100 x 15) = 9375 pi, so pi x R squared x 15 = 9375 pi gives R squared = 625 and R = 25 cm.
Correct Answer: 84
The wire radius is 0.05 cm, so its cross-section is pi x 0.0025 cm2 and the length is 66 over that area = 8400 cm = 84 m.
Correct Answer: 306.24 cm3
The external radius is 5.6 + 0.4 = 6 cm, so the metal volume is pi x (36 - 31.36) x 21 = 306.24 cm3.
Correct Answer: 44.0625 cm
The hollow cylinder volume is pi x (36 - 5.75 squared) x 15 = 44.0625 pi, and the solid cylinder cross-section is pi x 1 squared, so the length is 44.0625 cm.
Correct Answer: 3.696 kg
The iron volume is pi x (16 - 9) x 21 = 462 cm3, and at 8 g per cm3 that weighs 3696 g = 3.696 kg.
Correct Answer: 1 mm
From pi x r squared x 40 = 61.6, the inner radius is 0.7 cm = 7 mm, and the outer radius is 8 mm, so the thickness is 1 mm.
Topic Section
20 solved MCQs shown directly below
Correct Answer: 15 : 16
The cone volume is (1 over 3) pi x 9 x 5 = 15 pi and the cylinder volume is pi x 4 x 4 = 16 pi, so the ratio is 15 : 16.
Correct Answer: 136 pi cm2
The radius is 8 cm and the slant height is sqrt(15 squared + 8 squared) = 17 cm, so the curved surface is pi x 8 x 17 = 136 pi cm2.
Correct Answer: 498.35 cm2
The slant height is sqrt(14 squared + 7 squared) = 15.65 cm, so the total surface area is pi x 7 x (7 + 15.65) = 498.35 cm2.
Correct Answer: 16 pi cm3
Rotating about the 3 cm side gives radius 4 cm and height 3 cm, so the volume is (1 over 3) pi x 16 x 3 = 16 pi cm3.
Correct Answer: 60 pi m2
The radius is sqrt(10 squared - 8 squared) = 6 m, so the curved surface is pi x 6 x 10 = 60 pi m2 (the book prints cm2 in the options; the unit should be m2).
Correct Answer: 550 cm2
From (1 over 3) pi r squared x 24 = 1232, r = 7 cm, the slant height is sqrt(24 squared + 7 squared) = 25 cm, so the curved surface is pi x 7 x 25 = 550 cm2.
Correct Answer: 2.4 km
From pi r squared = 1.54, r = 0.7 km, so the height is sqrt(2.5 squared - 0.7 squared) = 2.4 km.
Correct Answer: 10010 cm2
From pi r squared = 3850, r = 35 cm, the slant height is sqrt(35 squared + 84 squared) = 91 cm, so the curved surface is pi x 35 x 91 = 10010 cm2.
Correct Answer: 862400 cm3
The slant height is 40040 over (pi x 70) = 182 cm, the height is sqrt(182 squared - 70 squared) = 168 cm, so the volume is (1 over 3) pi x 4900 x 168 = 862400 cm3.
Correct Answer: 10 cm
With r = 3x and h = 4x, (1 over 3) pi x 9x squared x 4x = 12 pi x cubed = 96 pi gives x = 2, so r = 6 cm and h = 8 cm, and the slant height is 10 cm.
Correct Answer: 525 m
From pi r squared = 346.5, r = 10.5 m, the slant height is sqrt(14 squared + 10.5 squared) = 17.5 m, the curved surface is pi x 10.5 x 17.5 = 577.5 m2, and 577.5 over 1.1 = 525 m of canvas.
Correct Answer: 8 times
Volume scales with radius squared times height, so doubling both gives 2 squared x 2 = 8 times.
Correct Answer: 72%
The new volume factor is 1.2 cubed = 1.728, an increase of 72.8%, given as 72% among the options.
Correct Answer: decreases by 25%
The height factor is 3 and the radius factor is 0.5, so the volume factor is 3 x 0.25 = 0.75, a decrease of 25%.
Correct Answer: 1 : 2
Volume is proportional to height when the radius is fixed, so doubling the height doubles the volume, a ratio of 1 : 2.
Correct Answer: 3 : 1
Volume ratio = (3 squared x 1) : (1 squared x 3) = 9 : 3 = 3 : 1.
Correct Answer: 1 : 4
With equal volumes, height is inversely proportional to radius squared, so the height ratio is 1 over 4 : 1 over 1 = 1 : 4.
Correct Answer: 25 : 64
Height ratio = (volume ratio) over (diameter ratio squared) = (1 over 4) over (16 over 25) = 25 : 64.
Correct Answer: 89.8 cm3
The largest cone has radius 3.5 cm and height 7 cm, so its volume is (1 over 3) pi x 12.25 x 7 = 89.8 cm3.
Correct Answer: 17 : 9
With r = 5x and h = 12x, the slant height is 13x, so the cylinder total surface is 2 pi x 5x x 17x = 170 pi x squared and the cone total surface is pi x 5x x 18x = 90 pi x squared, a ratio of 170 : 90 = 17 : 9.
Source & verification
Built by GK360 from verified bank questions — every answer rechecked before publishing.
Questions
48 questions, published of 50 printed in the book. Two items were dropped, never inferred: one whose standard volume matches no printed option, and one whose block dimensions are printed incompletely, so its wasted percentage cannot be found.
Cube edge, volume and surface-area ratios; cylinder volumes, curved and total surface areas, wells, tanks, pipes, hollow tubes and rollers, wire drawing and melting coins; and cone volumes, curved and total surface areas, slant heights, conical tents and mountains, scaling and ratio problems, and the largest cone cut from a cube.
Yes. Every answer was re-solved from scratch — cube-root and square scaling, cylinder and cone volume and surface-area formulas, annulus volumes for hollow pipes and rollers, and ratio algebra — and checked against the book's printed Answer Key on p. 773. 24 key errors were corrected to the standard answer, including a key letter that does not exist among the options, and two unanswerable items were dropped.
Volume and surface-area problems appear in the arithmetic and general-ability sections of FPSC, PPSC, NTS, PTS and CSS MPT one-paper exams, so the same formulas and scaling rules apply across all of them.
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