A. Read each problem, then solve using the formula. 1. Alice has a paperweight in the shape of a pyramid. Its height is 6 cm, length is 5.2 cm and width is 4.9 cm. What is its volume? 2. A juice container has a base area of 34 cm² and a height of 12.2 cm. What is its volume? B. Use any strategy to solve each problem. wide high? 1. How much space in a room will a cabinet occupy if it is 1.9m long, 0.61m and 2.74m 2. A box is 3.5 dm long and 6 dm high. Its volume is 210 dm³. How 3. A rectangular container is 0.4m long, 0.3m wide and 1 m high. What is its volume in cubic wide is it? cm?
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Answer:
A.
1. Volume of pyramid = (1/3) × base area × height
Base area = length x width / 2
Volume = (1/3) × (5.2 cm × 4.9 cm / 2) × 6 cm
= 51.0667 cm³
2. Volume of cylinder = base area × height
Volume = 34 cm² × 12.2 cm
= 415.6 cm³
B.
1. To find the volume of the cabinet, we multiply the length, width, and height together:
Volume = 1.9m × 0.61m × 2.74m
= 3.8451 m³
2. To find the width of the box, we need to divide the volume by the length and height:
Volume = length x width x height
width = Volume / (length x height)
width = 210 dm³ / (3.5 dm x 6 dm)
= 10 dm
3. To find the volume of the container, we simply multiply the length, width, and height together:
Volume = 0.4m × 0.3m × 1m
= 0.12 m³ or 120 cm³
A.
1. Alice has a paperweight in the shape of a pyramid. Its height is 6 cm, length is 5.2 cm and width is 4.9 cm. What is its volume?
Formula
V = (1/3) x base area x height
Given
Height = 6 cm
Length = 5.2 cm
Width = 4.9 cm
Solution
Base area = Length x Width
Base area = 5.2 cm x 4.9 cm
Base area = 25.48 cm²
V = (1/3) x 25.48 cm² x 6 cm
V = 127.4 cm³
2. A juice container has a base area of 34 cm² and a height of 12.2 cm. What is its volume?
Formula
V = base area x height
Given
Base area = 34 cm²
Height = 12.2 cm
Solution
V = 34 cm² x 12.2 cm
V = 414.8 cm³
B.
1. How much space in a room will a cabinet occupy if it is 1.9m long, 0.61m and 2.74m
Given
Length = 1.9 m
Width = 0.61 m
Height = 2.74 m
Solution
Volume = Length x Width x Height
Volume = 1.9 m x 0.61 m x 2.74 m
Volume = 3.56 m³
2. A box is 3.5 dm long and 6 dm high. Its volume is 210 dm³.
Given
Length = 3.5 dm
Height = 6 dm
Volume = 210 dm³
Solution
Volume = Length x Width x Height
Rearranging for width:
Width = Volume / (Length x Height)
Width = 210 dm³ / (3.5 dm x 6 dm)
Width = 10 dm
3. A rectangular container is 0.4m long, 0.3m wide and 1 m high. What is its volume in cubic wide is it? cm?
Given:
Length = 0.4 m
Width = 0.3 m
Height = 1 m
Solution
Volume = Length x Width x Height
Volume = 0.4 m x 0.3 m x 1 m
Volume = 0.12 m³
Convert
1 m³ = 1,000,000 cm³
Volume (in cm³) = Volume m³ x 1,000,000
Volume (in cm³) = 0.12 m³ x 1,000,000
Volume (in cm³) = 120,000 cm³