Match each three-dimensional figure to its volume based on the given dimensions. (Assume π = 3.14.)

2 answers:

8 0

The figures correspond to the following volumes: A right cylinder with a radius of 4 cm and height of 3 cm has a volume of 150.72 cu cm. A pyramid with a base area of 16 sq cm and a height of 30 cm holds a volume of 160 cu cm. Another pyramid featuring a square base of length 3 cm and height 16 cm amounts to a volume of 48 cu cm. Lastly, a cone with a radius of 5 cm and height of 12 cm has a volume of 314 cu cm.

tester [12.3K]2 months ago

3 0

The volume of the cylinder measures 150.72 cm³ (last answer). The cone's volume is 314 cm³ (1st answer). The pyramid's volume is 160 cm³ (2nd answer). The third pyramid has a volume of 48 cm³ (3rd answer). Step-by-step explanation: Let's review the volumes of some geometric shapes. The formula for the volume of a cylinder with radius r and height h is: V = π r² h. The volume for a cone with radius r and height h is: V = 1/3 π r² h. The formula for the volume of a pyramid is: V = 1/3 × base area × height. Now, let's calculate: For a cylinder with a radius of 4 cm and a height of 3 cm, with π approximated to 3.14, we find: V = 3.14 (4)² (3) = 150.72 cm³. Thus, the cylinder's volume is 150.72 cm³. For a cone with a radius of 5 cm and height of 12 cm: V = 1/3 (3.14) (5)² (12) = 314 cm³. So, the cone’s volume is 314 cm³. For a pyramid with a base area of 16 cm² and a height of 30 cm: V = 1/3 (16) (30) = 160 cm³, making the volume for this pyramid 160 cm³. Finally, for another pyramid with a base length of 3 cm and height of 16 cm: V = 1/3 (9) (16) = 48 cm³, obtaining a pyramid volume of 48 cm³.

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Then we will assign a variable to represent the value and also shift the repeating segment to the left.

Essentially, the concept here is that we can denote the repeating portion with a variable, let's say "x", and move forward with the calculation;

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$\bf thus\qquad \begin{array}{llll}
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you can verify that using your calculator.

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