3.9 Review

  1. Convert the following to the indicated measurements. Round to the nearest hundredth where necessary.

    a) 1.5 dam =                      m

     

     

     

    		 b) 3 hL =                      L

     

     

     

    		 c) 50 cm =                      mm

     

     

     
    d) 2 qt =                      L

     

     

     

    		 e) 250 g =                      kg

     

     

     

    		 f) 2 miles =                      km

     

     

     
    g) 2.5 hg =                      kg

     

     

     

    		 h) 500 cm =                   dm

     

     

     

    		 i) 3.5 lb =                      oz

     

     

     
    j) 100 yd =                      m

     

     

     

    		 k) 1.2 kg =                      lb

     

     

     

    		 l) 5 gal =                      L

     

     

     
    m) 10 mi =                      km

     

     

     

    		 n) 200 cm =                      m

     

     

     

    		 o) 8 lb =                      oz

     

     

     

  2. For each of the following word problems, convert to the indicated measurement. Round to the nearest hundredth where necessary.

    a) A table is 8 feet long. Convert the length to inches.

     

     

     

    		 b) Alia passed a football 24 yards. Convert the pass length to metres.

     

     

     
    c) A dog weighs 12 pounds. Convert the weight to ounces.

     

     

     

    		 d) A bag of flour weighs 3 kilograms. Convert the weight to grams.

     

     

     
    e) A truck weighs 8 tons. Convert the weight to pounds.

     

     

     

    		 f) A 5K run is 5 kilometres long. Convert this length to miles.

     

     

     
    g) A bookshelf is 5 feet 6 inches tall. Convert the height to inches.

     

     

     

    		 h) A watermelon weighs 10 lb 8 oz. Convert the weight to ounces

     

     

     

  3. Answer the following questions. Round to the nearest hundredth where necessary.

    a) A rectangular room is 15 feet wide by 14 feet long. Find the perimeter.

     

     

     

     

    		 b) A square has an area of 25 m2. What is the perimeter of the square?

     

     

     

     
    c) Brian wants to put a fence around his triangular flowerbed. The sides of the flowerbed are 6 feet, 8 feet, and 10 feet. The fence costs $10 per foot. How much will it cost for Brian to fence in his flowerbed?

     

     

     

     

    		 d) Find the area.

    A geometric shape is shown. A triangle is attached to a semi-circle. The height of the triangle is labeled 4. The base of the triangle, also the diametre of the semi-circle, is labeled 4.

     

     
    e) A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides 250 feet long, and the triangles are isosceles right triangles. Find the area of the park.

    A square is shown with four triangles coming off each side.

    		 f) The circumference of a circle is 20.4203 ft. Find the diameter of the circle.

     

     

     

     

     
    g) A circle has a diameter of 82.31 cm. Find the area.

     

     

     

     

    		 h) A driveway is in the shape of a rectangle 2000 cm wide by 35 m long. Find the area.

     

     

     

     
    i) Find the perimeter.

    A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.

    		 j) Find the area.

    A geometric shape is shown. It is an L-shape. The base is labeled 10, the right side 1, the top and left side are each labeled 4.

     

     

  4. In the following exercises, find the a) volume and b) surface area of each figure. Round to the nearest hundredth where necessary.

    a) A rectangular solid with a length of 14 centimetres, a width of 4.5 centimetres, and a height of 10 centimetres.

     

     
    b) A cube of tofu with sides measuring 2.5 inches.

     

     
    c) A cylinder with a radius of 2 yards and a height of 6 yards.

     

     
    d) A juice can with a diameter of 8 centimetres and a height of 15 centimetres.

     

     

     

  5. A triangular prism has a height of 20 cm. The triangular bases have a height of 3 cm and a base of 12 cm. Find the volume of the prism.

     

     

     

  6. In a right triangle, the angle opposite a side is 30°, and the hypotenuse measures 10 cm. What is the length of the side opposite the 30° angle?

     

     

     

  7. In a right triangle, one of the angles is 45°, and the side adjacent to this angle is 5 cm long. What is the length of the hypotenuse? Round to the nearest hundredth.

     

     

     

  8. In a right triangle, one angle is 60°, and the side opposite this angle is 8 cm long. How long is the adjacent side? Round to the nearest hundredth.

     

     

     

  9. In a right triangle, the side opposite an angle is 7 cm, and the side adjacent to the angle is 24 cm long. What is the measure of the angle? Round to the nearest hundredth.

     

     

     

  10. Given a right triangle, the side opposite an unknown angle has a length of 5 units, and the hypotenuse measures 13 units. Calculate the unknown angle. Round to the nearest hundredth.

     

     

     

  11. In a right triangle, the length of the adjacent side is 8 metres long, and the hypotenuse is 10 metres long. What is the angle between the adjacent side and the hypotenuse? Round to the nearest hundredth.

     

     

     

  12. A ladder is leaning against a wall. The angle between the ladder and the ground is 50°, and the distance from the base of the ladder to the wall is 6 metres. How long is the ladder? Round to the nearest tenth.

     

     

     

  13. A tree casts a shadow of 15 feet. The angle of elevation from the tip of the shadow to the top of the tree is 60°. How tall is the tree? Round to the nearest hundredth.

     

     

     

  14. From a point on the ground, the angle of elevation to the top of a building is 40°. If the distance from the point on the ground to the top of the building is 60 metres, how tall is the building? Round to the nearest hundredth.

     

     

     

  15. A drone is flying at an altitude of 100 metres. It is hovering over a point that is 200 metres away horizontally from a building. The angle of depression from the drone to the top of the building is θ. What is the angle of depression θ? Round to the nearest whole number.

     

     

     

  16. A person is standing 50 metres from the base of a mountain. The person looks up at the top of the mountain, and the angle of elevation is θ. If the height of the mountain is 150 metres, what is the angle of elevation θ? Round to the nearest whole number.

     

     

     

Answers

1.

a) 15 m b) 300 L c) 500 mm d) 1.89 L e) 0.25 kg
f) 3.22 km g) 0.25 kg h) 50 dm i) 56 oz j) 91.44 m
k) 2.65 lb l) 18.93 L m) 16.09 km n) 2 m o) 128 oz

2.

a) 96 in b) 38.62 m c) 192 oz d) 3 000 g
e) 16 000 lb f) 3.11 mi g) 66 in h) 168 oz

3.

a) 58 ft b) 20 m c) $240 d) 14.28 units2 e) 187 500 ft2
f) 6.50 ft g) 5 321.02 cm2 h) 700 m2 i) 26.85 units j) 22 units2

4.

a) V = 630 cm3
SA = 496 cm2		 b) V = 15.63 in3
SA = 37.5 in2		 c) V = 75.4 yd3
SA = 100.53 yd2		 d) V = 753.98 cm3
SA = 477.52 cm2
5. 360 cm3 6. 5 cm 7. 7.07 cm 8. 4.62 cm 9. 16.26° 10. 22.62°
11. 36.87° 12. 9.3 m 13. 25.98 ft 14. 38.57 m 15. 27° 16. 72°

Attribution

Unless otherwise indicated, material on this page has been adapted from the following resources:

Mazur, I. (2021). Introductory algebra. BCcampus. https://collection.bccampus.ca/textbooks/intermediate-algebra-bccampus-412/, licensed under CC BY 4.0

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Math 10C Workbook Copyright © 2026 by Leanne Thompson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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