Calculate the volume of a cuboid with length 6 cm, width 4 cm and height 3 cm.
(1)
2
Find the total surface area of a cube with side length 5 cm.
(1)
3
Convert 4200 cm3 to litres.
(1)
4
A triangular prism has a triangular cross-section of area 20 cm2 and length 9 cm. Calculate its volume.
(1)
5
Write down the number of faces of a triangular prism.
(1)
6
A cube has volume 27 cm3. Write down the length of one side.
(1)
7
Convert 2.5 m3 to litres (1 m3 = 1000 litres).
(1)
8
A triangular prism has a triangular end with base 10 cm and height 6 cm. The prism length is 15 cm. Calculate the volume of the prism.
(2)
9
Find the total surface area of a cuboid with dimensions 3 m by 4 m by 5 m.
(2)
10
A rectangular pool is 10 m long, 3 m wide and 2 m deep. How many litres of water does it hold when full? (1 m3 = 1000 litres)
(2)
11
A prism has a regular hexagon cross-section of area 24 cm2 and length 10 cm. Calculate its volume, then convert your answer to litres.
(2)
12
A cuboid box measures 30 cm by 20 cm by 15 cm. A label is stuck on one of the 30 cm by 20 cm faces. Calculate the fraction of the total surface area that the label's face covers.
(2)
13
Calculate the volume of a cylinder approximated as a prism, using area of circular cross-section. A cylinder has radius 5 cm and height 12 cm. Use π = 3.14.
(2)
14
A triangular prism has a triangular end with sides 9 cm, 12 cm and 15 cm. The prism is 20 cm long. Show that the triangular end is right-angled, then calculate the volume of the prism.
(3)
15
A metal beam is a triangular prism. The triangular end is isosceles with base 10 cm and equal sides 13 cm. The beam is 25 cm long. Calculate the volume of the beam.
(3)
16
A manufacturer makes an open-top box by cutting 5 cm squares from the corners of a 40 cm by 25 cm sheet of card and folding up the sides. Calculate the volume of the box.
(3)
17
A prism has a triangular cross-section with base 14 cm and area 63 cm2. Calculate the height of the triangle, then the volume of the prism if its length is 16 cm.
(3)
18
A solid is made by joining two identical rectangular prisms, each 5 cm by 3 cm by 2 cm, along a 5 cm by 3 cm face.
(a)Calculate the total volume of the solid.(2)
(b)Calculate the total external surface area of the solid.(2)
19
Aiden pours water into a triangular-prism-shaped tank. The triangular cross-section has base 8 m and height 3 m. The tank is 6 m long. Aiden pours in 54000 litres of water.
(a)Find the cross-sectional area of the triangular end.(1)
(b)Convert 54000 litres of water to m3.(1)
(c)The water forms a smaller prism with the same triangular cross-section as the tank. Find how far along the 6 m length of the tank the water reaches.(3)
Mark scheme · KS3.M-G12D Volume and Surface Area of Prisms: Fluency and Exam Drill
Question 1
B1 72 cao
Answer: 72 cm3
Question 2
B1 150 cao
Answer: 150 cm2
Question 3
B1 4.2 cao
Answer: 4.2 litres
Question 4
B1 180 cao
Answer: 180 cm3
Question 5
B1 5 cao
Answer: 5
Question 6
B1 3 cao
Answer: 3 cm
Question 7
B1 2500 cao
Answer: 2500 litres
Question 8
M1 find triangle area, 0.5 x 10 x 6 = 30
A1 450 cao
Answer: 450 cm3
Question 9
M1 2(3x4 + 3x5 + 4x5) or equivalent method
A1 94 cao
Answer: 94 m2
Question 10
M1 find volume, 10 x 3 x 2 = 60 m3
A1 60000 cao
Answer: 60000 litres
Question 11
M1 find volume, 24 x 10 = 240 cm3
A1 0.24 cao
Answer: 240 cm3 = 0.24 litres
Question 12
M1 find total surface area 2(30x20+30x15+20x15) = 2700 and one face area 600
A1 2/9 cao
Answer: 2/9
Question 13
M1 cross-section area 3.14 x 52 = 78.5
A1 942 cao
Answer: 942 cm3
Question 14
M1 show 92 + 122 = 81 + 144 = 225 = 152, confirming a right angle
M1 find triangle area, 0.5 x 9 x 12 = 54
A1 1080 cao
Answer: 1080 cm3
Question 15
M1 find the triangle's height using Pythagoras: √132 - 52 = √144 = 12
M1 find triangle area, 0.5 x 10 x 12 = 60
A1 1500 cao
Answer: 1500 cm3
Question 16
M1 find new base dimensions 40 - 10 = 30 and 25 - 10 = 15
M1 find base area, 30 x 15 = 450
A1 2250 cao
Answer: 2250 cm3
Question 17
M1 rearrange area formula, height = 2 x 63 / 14
M1 height = 9, then find volume 63 x 16
A1 1008 cao
Answer: 1008 cm3
Question 18
(a) M1 find the volume of one prism, 5 x 3 x 2 = 30
(a) A1 60 cao
(a) Answer: 60 cm3
(b) M1 find one prism's surface area 2(5x3+5x2+3x2) = 62, double it, then subtract the two joined 5x3 faces (2x15)
(b) A1 94 cao
(b) Answer: 94 cm2
Question 19
(a) B1 12 cao
(a) Answer: 12 m2
(b) B1 54 cao
(b) Answer: 54 m3
(c) M1 recognise volume = cross-sectional area x length, so length = volume / area