Grade 10 Maths · Measurement

Calculate surface area of a solid

Find the total outside area of a solid by adding the areas of all its faces, for example a cube with 3 cm sides: 6 × 9 = 54 cm².

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Surface Area and Volume: CubeKevinmathscience

How to Find the Surface Area of a Rectangular PrismMath with Mr. J

How to Find the Surface Area of a Triangular PrismMath with Mr. J

Surface Area and Volume: CylinderKevinmathscience

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Question 8.4 · 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}

$Diagram for this question$

8.4 Determine the total surface area of the container.(3)

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

More past paper questions: calculate surface area of a solid

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3. Question 7.2 · November 2025 · Paper 2 · Provincial · 3 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 $784$ cm $^{2}$ . The length of the width is $x$ cm.

$P = 2 l + 2 b$
$A = l \times b$
$V = l bh$
$S A = 2 l b + 2 l h + 2 bh$ $Diagram for this question$
7.2 Write an expression for the total surface area of the rectangular box in terms of $x$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Correct substitution $S A = 2 (2 x \times x) + 2 (x (3 + x)) + 2 (2 x (3 + x))$
  1 mark · Calculate surface area of a solid
2. ✓
  Simplification $= 4 x^{2} + 6 x + 2 x^{2} + 12 x + 4 x^{2}$
  1 mark · Multiply out a single bracket
3. ✓
  Answer $= 10 x^{2} + 18 x$
  1 mark · Collect like terms
4. Question WE10 · Siyavula Grade 10 Mathematics, 13.3 Right pyramids, right cones and spheres, Worked example 10 · 3 marks
$Diagram for this question$
WE10 Find the surface area of the following sphere (correct to 1 decimal place):(3)
Show the memo (3 ticks)Memo
1. ✓
  Formulasurface area of sphere $= 4 π r^{2}$
  1 mark · Calculate surface area of a solid
2. ✓
  Substitution $= 4 π (5)^{2} = 100 π$
  1 mark · Calculate surface area of a solid
3. ✓
  Answer $= 314, 2 cm^{2}$
  1 mark · Calculate surface area of a solid
5. Question WE2 · Siyavula Grade 10 Mathematics, 13.2 Right prisms and cylinders, Worked example 2 · 3 marks
$Diagram for this question$
WE2 Find the surface area of the following rectangular prism:(3)
Show the memo (3 ticks)Memo
1. ✓
  Large rectangleSketch the net: one large rectangle (the four side faces) and two small rectangles (the ends).
  large rectangle $=$ perimeter of small rectangle $\times$ length
  $= (2 + 5 + 2 + 5) \times 10 = 14 \times 10 = 140 cm^{2}$
  1 mark · Calculate surface area of a solid
2. ✓
  Two small rectangles $2 \times$ small rectangle $= 2 (5 \times 2) = 2 (10) = 20 cm^{2}$
  1 mark · Calculate surface area of a solid
3. ✓
  Answerlarge rectangle $+ 2 \times$ small rectangle $= 140 + 20 = 160$
  The surface area of the rectangular prism is $160 cm^{2}$ .
  1 mark · Calculate surface area of a solid
6. Question WE4 · Siyavula Grade 10 Mathematics, 13.2 Right prisms and cylinders, Worked example 4 · 3 marks
$Diagram for this question$
WE4 Find the surface area of the following cylinder (correct to 1 decimal place):(3)
Show the memo (3 ticks)Memo
1. ✓
  Curved surface (rectangle)area of large rectangle $=$ circumference of circle $\times$ length
  $= 2 π r \times l = 2 π (10) \times 30 = 1884, 9555 \dots cm^{2}$
  1 mark · Calculate surface area of a solid
2. ✓
  Area of a circlearea of circle $= π r^{2} = π (10)^{2} = 314, 1592 \dots cm^{2}$
  1 mark · Calculate surface area of a solid
3. ✓
  Answersurface area $=$ area large rectangle $+ (2 \times$ area of circle $)$
  $= 1884, 9555 \dots + 2 (314, 1592 \dots)$
  $= 2513, 3 cm^{2}$
  1 mark · Calculate surface area of a solid

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