Edexcel GCSE Maths (1MA1), Higher tier · Geometry and measures
Practise Plans and elevations. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy5 marks
The diagram shows a solid made from 5 centimetre cubes, all one layer high.
[object Object]
(a) On the centimetre grid, draw the plan of the solid.[2]
[object Object]
(b) Work out the surface area of the solid.[3]
Show the answer and mark scheme
(a)Answer: Two rows of squares: 3 squares in the back row and 2 squares in the front row, lined up on the left (■■■ / ■■□, back row first).
B2 for a correct plan: 3 squares in the back row and 2 in the front row, lined up on the left
Worked solution: Looking down on the solid, you see the top of each cube: the back row has 3 cubes and the front row has 2 cubes, lined up at the left.
(b)Answer: 20 cm²
M1 for the top and bottom: \(2 \times 5 = 10\)
M1 for counting the 10 exposed faces around the sides
A1 for 20 cao
Worked solution: Top and bottom: \(2 \times 5 = 10\) squares. Around the sides: the perimeter of the plan is 10 cm, and the solid is 1 cm high, so there are 10 more squares. Total \(= 10 + 10 = 20\) cm².
Question 2Medium5 marks
The diagram shows a solid made from centimetre cubes, stacked in columns on a square base with no gaps.
[object Object]
(a) Work out the volume of the solid.[1]
(b) Work out the surface area of the solid.[4]
Show the answer and mark scheme
(a)Answer: 8 cm³
B1 for 8 cao
Worked solution: The four columns have heights 3, 2, 2 and 1, so there are \(3 + 2 + 2 + 1 = 8\) cubes and the volume is 8 cm³.
(b)Answer: 28 cm²
M1 for the 4 squares on the top and the 4 squares on the base
M1 for 5 squares facing any one direction (e.g. the front: \(3 + 2\))
M1 for all 20 squares on the vertical faces
A1 for 28 cao
Worked solution: Top: the top of every column can be seen from above, so 4 squares. Base: 4 squares. Vertical faces: the view from the front shows columns of heights 3 and 2, so 5 squares face the front. In the same way 5 squares face the back, 5 face the left and 5 face the right: 20 squares. Surface area \(= 4 + 4 + 20 = 28\) cm².
Question 3Hard6 marks
A solid is made from cubes of edge 2 cm. The diagram shows the plan of the solid. The number on each square is the number of cubes stacked on that square. There are no gaps in the solid.
[object Object]
(a) Work out the volume of the solid.[2]
(b) Work out the surface area of the solid.[4]
Show the answer and mark scheme
(a)Answer: \(160\) cm³
M1 for 20 cubes \(\times 2^{3}\) (or \(20 \times 8\))
A1 for 160 cao
Worked solution: Number of cubes \(= 20\). Each cube has volume \(2^{3} = 8\) cm³, so the volume is \(20 \times 8 = 160\) cm³.
(b)Answer: \(256\) cm²
M1 for the top and bottom: \(2 \times 9 = 18\) faces
M1 for counting all the exposed side faces, including the steps between columns (46)
M1 for their total number of faces \(\times 2^{2}\) (\(64 \times 4\))
A1 for 256 cao
Worked solution: Top: 9 faces. Bottom: 9 faces. Sides, including every step between columns of different heights: 46 faces. Total \(= 64\) faces, each \(2 \times 2 = 4\) cm². Surface area \(= 64 \times 4 = 256\) cm².