Measures and solids · Ages 12–13
Prisms worksheet
Covers: Volume of a prism, Surface area of a prism, Prisms at work: capacity and water levels
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Prisms worksheet
Measures and solids · Ages 12–13
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The prism in the picture has a right-angled triangle as its cross-section, its two shorter sides 11 cm and 8 cm, and it is 16 cm long. What is its volume, in cm³?
Answer:
2.The prism in the picture has a volume of 960 cm³, and its cross-section is a triangle 12 cm across and 10 cm high. How long is the prism?
Answer:
3.The prism in the picture has an L-shaped cross-section, 14 cm wide and 12 cm high, both arms 2 cm thick, and it is 4 cm long. What is its volume, in cm³?
Answer:
4.The prism in the picture has a trapezium as its cross-section: 10 cm along the top, 14 cm along the bottom, 7 cm high. It is 16 cm long. What is its volume, in cm³?
Answer:
5.The prism in the picture has an isosceles triangle as its cross-section: 6 cm across, 4 cm high, its two equal sides 5 cm each; the prism is 18 cm long. What is its total surface area, in cm²?
Answer:
6.The prism in the picture has an L-shaped cross-section, 9 cm wide and 10 cm high, both arms 4 cm thick; it is 4 cm long. What is its total surface area, in cm²?
Answer:
7.The prism in the picture has a right-angled triangle with sides 9 cm, 12 cm and 15 cm as its cross-section, and a total surface area of 468 cm². How long is it?
Answer:
8.A cuboid tank is 80 cm long, 30 cm wide and 10 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?
Answer:
9.A tank has a base area of 200 cm². After 800 cm³ of water is poured in, by how many cm has the water level risen?
Answer:
10.A cuboid tank is 50 cm long and 10 cm wide inside, with water 5 cm deep. 9 L more is poured in, none spilling. How deep is the water now, in cm?
Answer:
11.A cuboid tank 25 cm long and 10 cm wide holds water 20 cm deep. All of it is poured into another, empty tank with a base area of 200 cm². How deep is the water now, in cm?
Answer:
Part B: Choose, or true or false (2 marks each)
12.Open out the three sides of the prism in the picture and they join into one rectangle, 13 cm wide. How long is the rectangle?
- A. 12 cm
- B. 6 cm
- C. 7 cm
- D. 25 cm
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A model house has a five-sided cross-section: a rectangle 8 cm wide and 6 cm high, with a triangular roof 8 cm across and 3 cm high on top; the house is 19 cm long. The rectangle is cm², the roof cm², and the house's volume cm³.
Fill in each blank
Working:
Answer:
14.A triangular chocolate bar is 15 cm long, its cross-section a triangle 4 cm across and 3 cm high. The cross-section is cm², one bar's volume cm³; a box of 6 bars holds cm³.
Fill in each blank
Working:
Answer:
15.A cuboid gift box is 13 cm long, 19 cm wide and 10 cm high. How many cm² of wrapping paper cover the whole box exactly (no overlaps)?
Working:
Answer:
16.A box is a triangular prism, its cross-section a right-angled triangle of sides 9 cm, 12 cm and 15 cm, and it is 15 cm long. The card it is made of costs $0.5 for each 100 cm². How many dollars of card does one box take?
Working:
Answer:
17.A cuboid pool 16 m long and 7 m wide is to be filled to a depth of 1.5 m. The hose pours in 500 L a minute. How many minutes does it take?
Working:
Answer:
18.A cuboid fish tank is 30 cm long and 16 cm wide inside. A pottery ornament of volume 1248 cm³ is put in, right under the water, and none spills. By how many cm does the water rise?
Working:
Answer:
Show the answers and working
Prisms worksheet: Answers and working
Part A: Working out and filling in
1. 704 cm³
Cross-section 11 × 8 ÷ 2 = 44 cm², volume = cross-section × length = 44 × 16 = 704 cm³.
2. 16 cm
The cross-section is 12 × 10 ÷ 2 = 60 cm², so the length = volume ÷ cross-section = 960 ÷ 60 = 16 cm.
3. 192 cm³
Split the L into two rectangles: the bottom arm 14 × 2 = 28 and the upright one 10 × 2 = 20, 48 cm²; volume 48 × 4 = 192 cm³.
4. 1344 cm³
The trapezium: (10 + 14) × 7 ÷ 2 = 84 cm²; volume 84 × 16 = 1344 cm³.
5. 312 cm²
The ends 2 × (6 × 4 ÷ 2) = 24; perimeter 6 + 5 + 5 = 16, sides 16 × 18 = 288; 312 cm² in all.
6. 272 cm²
The cross-section is 60 cm², two of them 120; the L's perimeter is the same as a 9 by 10 rectangle's, 2 × (9 + 10) = 38, so the sides are 38 × 4 = 152; 272 cm² in all.
7. 10 cm
The ends are 2 × 9 × 12 ÷ 2 = 108, so the sides are 468 − 108 = 360; the perimeter is 36 cm, so the length = 360 ÷ 36 = 10 cm.
8. 24 L
It holds 80 × 30 × 10 = 24000 cm³ = 24000 ÷ 1000 = 24 L.
9. 4 cm
The water poured in is a prism on the tank's base: rise = volume ÷ base area = 800 ÷ 200 = 4 cm.
10. 23 cm
9 L = 9000 cm³; the base is 50 × 10 = 500 cm², so the water rises 9000 ÷ 500 = 18 cm; now 5 + 18 = 23 cm deep.
11. 25 cm
The water's volume stays the same: 25 × 10 × 20 = 5000 cm³; the new depth = 5000 ÷ 200 = 25 cm.
Part B: Choose, or true or false
12. A. 12 cm
The three sides laid end to end make the cross-section's perimeter: 3 + 4 + 5 = 12 cm.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 48, 12, 1140
8 × 6 = 48; 8 × 3 ÷ 2 = 12; the cross-section is 60 cm², the volume 60 × 19 = 1140 cm³.
14. 6, 90, 540
4 × 3 ÷ 2 = 6; 6 × 15 = 90; 90 × 6 = 540.
15. 1134 cm²
Six faces, three pairs: 2 × (13 × 19 + 19 × 10 + 13 × 10) = 1134 cm².
16. 3.24 dollars
Total surface area 2 × 9 × 12 ÷ 2 + (9 + 12 + 15) × 15 = 648 cm², and 648 ÷ 100 × 0.5 = $3.24.
17. 336 minutes
The water: 16 × 7 × 1.5 = 168 m³ = 168000 L (1 m³ = 1000 L); 168000 ÷ 500 = 336 minutes.
18. 2.6 cm
The ornament's volume equals the water lifted: the base is 30 × 16 = 480 cm², so the rise is 1248 ÷ 480 = 2.6 cm.
Numsprite · numsprite.com/en/worksheets/prisms
Practise it in the gamePrisms · Unlimited questions, no download