4.12H Surface Area: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 70 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A cube has side length 7 cm. Work out the total surface area of the cube.

(Total for Question 1 is 2 marks)

A closed rectangular box has exterior dimensions 12 cm by 8 cm by 5 cm. Calculate the surface area of the box.

(Total for Question 2 is 3 marks)

A closed cylinder has radius 3 cm and height 10 cm. Work out the total surface area. Give your answer in terms of π.

(Total for Question 3 is 3 marks)

A solid is made by attaching a right circular cone to one circular face of a closed cylinder so that their bases coincide. The cylinder has radius 4 cm and height 9 cm. The cone has the same radius 4 cm and sloping height (l) 5 cm. Calculate the total surface area of the solid (do not include the area of the circle where they join). Give your answer in terms of π.

(Total for Question 4 is 4 marks)

A regular square pyramid has base side 10 cm and sloping height 13 cm. Calculate the total surface area of the pyramid.

(Total for Question 5 is 4 marks)

Show that if the dimensions of a solid are all multiplied by 3, its total surface area is multiplied by 9. You may use a cube or any prism as an example and justify your scaling step.

(Total for Question 6 is 3 marks)

A closed cylinder has total surface area 154 π cm² and radius 7 cm. Find its height. Give your answer in cm, correct to 1 decimal place if necessary.

(Total for Question 7 is 4 marks)

A solid model is made by placing a hemisphere on top of a right circular cone so that the flat face of the hemisphere rests on the cone base. The hemisphere has radius r, and the cone has the same base radius r and sloping height l. The curved surface area of the hemisphere is 2 π r² and the curved surface area of the cone is π r l. Given r = 6 cm and l = 10 cm, calculate the total exposed surface area of the model (do not include the circular area where they meet). Give your answer in terms of π.

(Total for Question 8 is 7 marks)

Mark scheme · 4.12H Surface Area: Higher Tier Practice

Question 1

M1 method for surface area 6 x side² or show 6 x 7²
A1 294 cm² cao
Answer: 294 cm²

Question 2

M1 method: 2(ab + ac + bc) or substitution 2(12*8 + 12*5 + 8*5)
M1 arithmetic for the three products summed (96 + 60 + 40 = 196) or equivalent
A1 392 cm² cao
Answer: 392 cm²

Question 3

M1 method: total area = 2(π r²) + 2(π r h) or substitute π*(2*r² + 2*r*h)
M1 substitute r=3, h=10 to get 2(π*9) + 2(π*3*10) = 18pi + 60pi
A1 78 π cm² cao
Answer: 78 π cm²

Question 4

M1 identify surfaces: curved surface of cylinder 2 π r h_cyl and curved surface of cone π r l, and one circular base of cylinder
M1 substitute r=4, h_cyl=9, l=5: cylinder curved = 2 π *4*9 = 72 π; cone curved = π*4*5 = 20 π; one base = π*4² = 16 π
M1 sum areas: 72 π + 20 π + 16 π
A1 108 π cm² cao
Answer: 108 π cm²

Question 5

M1 identify base area and 4 triangular faces: base = 10² = 100, each triangle area = 1/2 * base side * sloping height
M1 triangle area = 1/2 * 10 * 13 = 65, total for four faces = 4*65 = 260
M1 sum base + faces = 100 + 260
A1 360 cm² cao
Answer: 360 cm²

Question 6

M1 state surface area scales as length² so factor becomes k² when lengths scaled by k
M1 substitute k=3 to get scaling factor 3² = 9
A1 conclusion: total surface area multiplied by 9 with justification oe
Answer: Surface area scale factor = 3² = 9, so total surface area is multiplied by 9.

Question 7

M1 use formula 2 π r² + 2 π r h = total surface area and substitute r=7
M1 substitute 2 π *7² + 2 π *7 * h = 154 π, cancel π and compute 98 + 14 h = 154
M1 solve 14 h = 56 so h = 4
A1 h = 4 cm cao
Answer: 4 cm

Question 8

M1 identify curved areas: hemisphere 2 π r² and cone π r l and note base circle is hidden
M1 substitute r=6, l=10: hemisphere = 2 π *36 = 72 π, cone = π *6*10 = 60 π
M1 sum curved areas 72 π + 60 π = 132 π
M1 consider whether the flat circular face is exposed; state it is not included
A1 132 π cm² cao
SC1 alternative correct working showing hemisphere area as 2 π r² and cone area and summing to 132 π
SC1 final answer stated in terms of π
Answer: 132 π cm²

Surface Area: Higher Tier Practice - Worksheets, Questions and Revision