Grade 10 Maths · Measurement

Calculate the volume of a solid

Find how much space a solid takes up using the right formula, for example a cylinder with radius 2 cm and height 5 cm holds about 62,8 cm³.

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Surface Area and Volume: CylinderKevinmathscience

Surface Area and Volume Grade 9: ConeKevinmathscience

How to Find the Volume of Cylinders & PrismsCognito

Measurement Exam Questions | Gr 11 | Gr 10Kevinmathscience

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Question 7.4 · November 2025 · Paper 2 · Provincial · 2 marks

A closed rectangular box has a length(L) that is twice its width(W), and its height(H) is 3 cm more than its width. The surface area of the box is

784

^{2}

. The length of the width is

x

cm.

P = 2 l + 2 b

A = l \times b

V = l bh

S A = 2 l b + 2 l h + 2 bh

$Diagram for this question$

7.4 Calculate the volume of the box.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: calculate the volume of a solid

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3. Question 8.3 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram, a lid with a hemispherical form seals an open cone. The slanted height of the cone is 13 cm, the diameter of the cone and hemisphere is 10 cm, the height of the cone $h$ cm.

Formulae:
$V = \frac{2}{3} π r^{3}$ ; $V = \frac{1}{3} π r^{2} h$ ; Surface Area $= π r^{2} + π rs$ ; Surface Area $= 2 π r^{2}$ $Diagram for this question$
8.3 Calculate the volume of this container.(3)
Show the memo (3 ticks)Memo
1. ✓
  Correct formulaVolume $= \frac{2}{3} π r^{3} + \frac{1}{3} π r^{2} h$
  1 mark · Calculate the volume of a solid
2. ✓
  Substitution $= \frac{2}{3} π (5)^{3} + \frac{1}{3} π (5)^{2} (12)$
  1 mark · Calculate the volume of a solid
3. ✓
  Answer $= \frac{550}{3} π = 575, 96$ cm $^{3}$
  1 mark · Calculate the volume of a solid
4. Question 8.2 · November 2024 · Paper 2 · Provincial · 3 marks
A mine dumps its waste at a landfill site where it takes the shape of a cone shown in the diagram below. The radius of the circular base is $r$ meters, the height is $h$ meters and the angle between the slant height and the base of the cone is $50°$ .
The circumference of the landfill site is 245 meters.

Volume of cone $= \frac{1}{3} π r^{2} h$

Total surface area of cone $= π r^{2} + π rs$ $Diagram for this question$
8.2 Determine the volume of the mine waste, rounded to the nearest cubic meter.(3)
Show the memo (3 ticks)Memo
1. ✓
  FormulaVolume $= \frac{1}{3} π r^{2} h$
  1 mark · Calculate the volume of a solid
2. ✓
  Substitution $= \frac{1}{3} π (39)^{2} .46, 5$
  1 mark · Calculate the volume of a solid
3. ✓
  Answer $= 74065$ m $^{3}$
  1 mark · Calculate the volume of a solid
5. Question WE12 · Siyavula Grade 10 Mathematics, 13.3 Right pyramids, right cones and spheres, Worked example 12 · 3 marks
WE12 Find the volume of a square pyramid with a height of $3 cm$ and a side length of $2 cm$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $V = \frac{1}{3} \times b^{2} \times H$
  1 mark · Calculate the volume of a solid
2. ✓
  Substitution $b = 2$ and $H = 3$ :
  $V = \frac{1}{3} \times 2^{2} \times 3$
  1 mark · Calculate the volume of a solid
3. ✓
  Answer $V = \frac{1}{3} \times 12 = 4 cm^{3}$
  The volume of the square pyramid is $4 cm^{3}$ .
  1 mark · Calculate the volume of a solid
6. Question WE7 · Siyavula Grade 10 Mathematics, 13.2 Right prisms and cylinders, Worked example 7 · 3 marks
$Diagram for this question$
WE7 Find the volume of the following cylinder (correct to 1 decimal place):(3)
Show the memo (3 ticks)Memo
1. ✓
  Area of basearea of circle $= π r^{2} = π (4)^{2} = 16 π cm^{2}$
  1 mark · Calculate the volume of a solid
2. ✓
  Volume formula and substitutionvolume $=$ area of base $\times$ height
  $= π r^{2} \times h = 16 π \times 15$
  1 mark · Calculate the volume of a solid
3. ✓
  Answer $\approx 754, 0 cm^{3}$
  The volume of the cylinder is $754, 0 cm^{3}$ .
  1 mark · Calculate the volume of a solid

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