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Grade 10 · Measurement
Measurement: Surface Area, Volume & Scaling (Grade 10)
MARKING GUIDELINE
Marks
33
Duration
50 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 33
Instructions and Information
- Answer ALL the questions in this question paper.
- Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
- Show ALL calculations clearly.
- Show all units where applicable.
- Number the answers correctly according to the numbering system used in this question paper.
- A non-programmable calculator may be used, unless stated otherwise.
- Write neatly and legibly.
Question 1
[10 MARKS]Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.
- 1.1A cylinder has radius 5 cm and height 10 cm. Its VOLUME is …(1)A)785,40 cm³✓B)157,08 cm³C)314,16 cm³D)1 570,80 cm³Answer: A — V = πr²h = π × 25 × 10 = 785,40 cm³.
- B — used πrh instead of πr²h
- C — used 2πrh, which is the CURVED SURFACE area
- D — doubled the correct volume
- 1.2A sphere has radius 6 cm. Its VOLUME is …(1)A)904,78 cm³✓B)452,39 cm³C)678,58 cm³D)150,80 cm³Answer: A — V = (4/3)πr³ = (4/3) × π × 216 = 904,78 cm³.
- B — that is 4πr², the SURFACE AREA
- C — left out the factor of 4/3
- D — squared the radius instead of cubing it
- 1.3A cone has radius 3 cm and perpendicular height 8 cm. Its VOLUME is …(1)A)75,40 cm³✓B)226,19 cm³C)25,13 cm³D)150,80 cm³Answer: A — V = ⅓πr²h = (1/3) × π × 9 × 8 = 75,40 cm³.
- B — used πr²h — that is the CYLINDER, three times too big
- C — used ⅓πrh, forgetting to square the radius
- D — used two thirds instead of one third
- 1.4A closed cylinder has radius 4 cm and height 10 cm. Its TOTAL SURFACE AREA is …(1)A)351,86 cm²✓B)251,33 cm²C)301,59 cm²D)100,53 cm²Answer: A — TSA = 2πr² + 2πrh = 100,53 + 251,33 = 351,86 cm².
- B — gave only the CURVED surface, leaving out the two circular ends
- C — included only ONE circular end instead of two
- D — gave only the two ends, leaving out the curved surface
- 1.5If every dimension of a solid is multiplied by 3, its VOLUME is multiplied by …(1)A)27✓B)3C)9D)6Answer: A — Volume scales by k³, and 3³ = 27.
- B — that is the factor for a LENGTH
- C — that is the factor for an AREA
- D — doubled the factor instead of cubing it
- 1.6If every dimension of a solid is HALVED, its SURFACE AREA is multiplied by …(1)A)14✓B)12C)18D)4Answer: A — Area scales by k², and (½)² = ¼.
- B — that is the factor for a LENGTH
- C — that is the factor for a VOLUME
- D — halving makes the area smaller, not four times larger
- 1.7A rectangular prism measures 10 cm by 6 cm by 4 cm. Its VOLUME is …(1)A)240 cm³✓B)20 cm³C)248 cm²D)60 cm³Answer: A — V = length × breadth × height = 10 × 6 × 4 = 240 cm³.
- B — ADDED the three dimensions instead of multiplying them
- C — that is the total SURFACE AREA, and it is measured in cm²
- D — multiplied only two of the three dimensions
- 1.8A cube has volume 125 cm³. Its TOTAL SURFACE AREA is …(1)A)150 cm²✓B)25 cm²C)750 cm²D)30 cm²Answer: A — The side is ∛125 = 5 cm, and a cube has 6 faces of 25 cm² each.
- B — gave the area of ONE face only
- C — used the volume 125 in place of the face area 25
- D — multiplied the SIDE by 6 instead of the face AREA by 6
- 1.9A cylindrical tank has radius 0,5 m and height 2 m. Its capacity is …(1)A)1 570,80 litres✓B)1,57 litresC)15,71 litresD)157,08 litresAnswer: A — V = πr²h = 1,57 m³, and 1 m³ = 1 000 litres.
- B — left the answer in cubic METRES instead of converting to litres
- C — multiplied by 10 instead of by 1 000
- D — multiplied by 100 instead of by 1 000
- 1.10A square pyramid has base side 6 cm and perpendicular height 10 cm. Its VOLUME is …(1)A)120 cm³✓B)360 cm³C)60 cm³D)20 cm³Answer: A — V = ⅓ × base area × height = (1/3) × 36 × 10 = 120 cm³.
- B — used base area × height — that is the PRISM, three times too big
- C — used 6 × 10, forgetting both the third and the square
- D — used ⅓ × 6 × 10, forgetting to square the base side
Answer grid — marking guideline
| 1.1 | A | B | C | D |
| 1.2 | A | B | C | D |
| 1.3 | A | B | C | D |
| 1.4 | A | B | C | D |
| 1.5 | A | B | C | D |
| 1.6 | A | B | C | D |
| 1.7 | A | B | C | D |
| 1.8 | A | B | C | D |
| 1.9 | A | B | C | D |
| 1.10 | A | B | C | D |
Question 2
[10 MARKS]A cylindrical water tank has a radius of 5 m and a height of 12 m. Use π ≈ 3,14 and round off to TWO decimal places where necessary.
- 2.1Calculate the volume of the tank.(3)V = πr2h = 3,14 × 25 × 12 (2) = 942 m3 (1)
- 2.2Calculate the total surface area of the tank.(4)SA = 2πr2 + 2πrh (1)
= 157 + 376,8 (2) = 533,80 m2 (1) - 2.31 m3 holds 1 000 litres. Determine the capacity of the tank in litres.(3)942 × 1 000 (2) = 942 000 litres (1)
Question 3
[13 MARKS]The diagram below shows a cone with a base radius of 3 cm and a perpendicular height of 4 cm, and a sphere with a radius of 6 cm. Use π ≈ 3,14, Vcone = 13πr2h, Vsphere = 43πr3 and SAsphere = 4πr2.
- 3.1Calculate the volume of the cone.(3)V = 13 × 3,14 × 9 × 4 (2) = 37,68 cm3 (1)
- 3.2Calculate the volume and the surface area of the sphere.(4)V = 43 × 3,14 × 216 = 904,32 cm3 (2)
SA = 4 × 3,14 × 36 = 452,16 cm2 (2) - 3.3ALL the dimensions of the cone are doubled. Determine by what factor its volume increases, and justify your answer.(4)Both r and h double (1)
V depends on r2h, so the factor is 22 × 2 (2)
The volume becomes 8 times as big (1) - 3.4Explain why doubling the dimensions multiplies the SURFACE AREA by only 4.(2)Surface area depends on TWO dimensions (1), so it grows by the square of the factor, 22 (1)
TOTAL: 33 marks
This question paper consists of 3 questions.