21M.1.SL.TZ1.3

pestleMathematicsAISLPaper 121M· sl-3-1-3d-space-volume-angles-midpointssource ↗

A piece of candy is made in the shape of a solid hemisphere. The radius of the hemisphere is $6 mm$ .

Calculate the total surface area of one piece of candy.

[4]

The total surface of the candy is coated in chocolate. It is known that $1$ gram of the chocolate covers an area of $240 {mm}^{2}$ .

Calculate the weight of chocolate required to coat one piece of candy.

[2]

Markscheme / solution

$\frac{1}{2} \times 4 \times π \times 6^{2} + π \times 6^{2}$ OR $3 \times π \times 6^{2}$ (M1)(A1)(M1)

Note: Award M1 for use of surface area of a sphere formula (or curved surface area of a hemisphere), A1 for substituting correct values into hemisphere formula, M1 for adding the area of the circle.

$= 339 {mm}^{2} (108 π, 339.292 \dots)$ A1

[4 marks]

$\frac{339.292 \dots}{240}$ (M1)

$= 1.41 (g) (\frac{9 π}{20}, 0.45 π, 1.41371 \dots)$ A1

[2 marks]

Examiners’ report

[N/A]