A rectangular solid is 24.9 cm long, 20.3 cm wide, and 19.6 cm high. By rounding off appropriately, select which of the values A, B, C, or D is the best estimate for the volume of the solid. A 1000 cm³ B 100 cm³ C 10 000 cm³ D 65 cm³ Estimation: Best estimate: (ii) Using a calculator, or otherwise, calculate the exact volume of the solid in cm³.

Photo AI

A rectangular solid is 24.9 cm long, 20.3 cm wide, and 19.6 cm high - Junior Cycle Mathematics - Question 6 - 2014

Question 6

A rectangular solid is 24.9 cm long, 20.3 cm wide, and 19.6 cm high. By rounding off appropriately, select which of the values A, B, C, or D is the best estimate for... show full transcript

Worked Solution & Example Answer:A rectangular solid is 24.9 cm long, 20.3 cm wide, and 19.6 cm high - Junior Cycle Mathematics - Question 6 - 2014

Step 1

Estimation: Calculate Volume with Rounded Dimensions

96%

114 rated

Answer

To estimate the volume, we round the dimensions to the nearest centimeter:

Length: 24.9 cm rounds to 25 cm
Width: 20.3 cm rounds to 20 cm
Height: 19.6 cm rounds to 20 cm

The formula for the volume of a rectangular solid is given by:

Volume = length imes width imes height

Substituting the rounded dimensions gives us:

Volume ext{ (estimated)} = 25 imes 20 imes 20 = 10,000 ext{ cm}^3

Thus, the best estimate for the volume of the solid is option C: 10,000 cm³.

Step 2

Using a calculator, or otherwise, calculate the exact volume of the solid in cm³.

99%

104 rated

Answer

To calculate the exact volume, we use the original dimensions:

Length: 24.9 cm
Width: 20.3 cm
Height: 19.6 cm

Using the volume formula:

Volume = length imes width imes height

We substitute the exact values:

Volume = 24.9 imes 20.3 imes 19.6 = 9,907.212 ext{ cm}^3

Therefore, the exact volume of the solid is 9,907.212 cm³.

Join the Junior Cycle students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;