Math / Geometry

Question9. A cardboard box measures 40 cm by 40 cm by 30 cm . Calculate 6 length of the space diagonal, to the nearest centimetre.

Studdy Solution

STEP 1

1. The box is a rectangular prism with dimensions $40 \, \text{cm} \times 40 \, \text{cm} \times 30 \, \text{cm}$ .
2. The space diagonal is the longest diagonal that runs from one corner of the box to the opposite corner.

STEP 2

1. Recall the formula for the space diagonal of a rectangular prism.
2. Substitute the given dimensions into the formula.
3. Calculate the length of the space diagonal.
4. Round the result to the nearest centimeter.

STEP 3

Recall the formula for the space diagonal of a rectangular prism:
$d = \sqrt{l^2 + w^2 + h^2}$
where $l$ , $w$ , and $h$ are the length, width, and height of the prism, respectively.

STEP 4

Substitute the given dimensions into the formula:
$d = \sqrt{40^2 + 40^2 + 30^2}$

STEP 5

Calculate the length of the space diagonal:
$d = \sqrt{40^2 + 40^2 + 30^2}$ $= \sqrt{1600 + 1600 + 900}$ $= \sqrt{4100}$ $\approx 64.03$

STEP 6

Round the result to the nearest centimeter:
$d \approx 64 \, \text{cm}$
The length of the space diagonal is:
$\boxed{64 \, \text{cm}}$

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Question9. A cardboard box measures 40 cm by 40 cm by 30 cm . Calculate 6 length of the space diagonal, to the nearest centimetre.

Studdy Solution

STEP 1

1. The box is a rectangular prism with dimensions $40 \, \text{cm} \times 40 \, \text{cm} \times 30 \, \text{cm}$ .
2. The space diagonal is the longest diagonal that runs from one corner of the box to the opposite corner.

STEP 2

1. Recall the formula for the space diagonal of a rectangular prism.
2. Substitute the given dimensions into the formula.
3. Calculate the length of the space diagonal.
4. Round the result to the nearest centimeter.

STEP 3

Recall the formula for the space diagonal of a rectangular prism:
$d = \sqrt{l^2 + w^2 + h^2}$
where $l$ , $w$ , and $h$ are the length, width, and height of the prism, respectively.

STEP 4

Substitute the given dimensions into the formula:
$d = \sqrt{40^2 + 40^2 + 30^2}$

STEP 5

Calculate the length of the space diagonal:
$d = \sqrt{40^2 + 40^2 + 30^2}$ $= \sqrt{1600 + 1600 + 900}$ $= \sqrt{4100}$ $\approx 64.03$

STEP 6

Round the result to the nearest centimeter:
$d \approx 64 \, \text{cm}$
The length of the space diagonal is:
$\boxed{64 \, \text{cm}}$

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Question9. A cardboard box measures 40 cm by 40 cm by 30 cm . Calculate 6 length of the space diagonal, to the nearest centimetre.

Studdy Solution

STEP 1

1. The box is a rectangular prism with dimensions 40 cm×40 cm×30 cm 40 \, \text{cm} \times 40 \, \text{cm} \times 30 \, \text{cm} 40cm×40cm×30cm.2. The space diagonal is the longest diagonal that runs from one corner of the box to the opposite corner.

STEP 2

1. Recall the formula for the space diagonal of a rectangular prism.2. Substitute the given dimensions into the formula.3. Calculate the length of the space diagonal.4. Round the result to the nearest centimeter.

STEP 3

Recall the formula for the space diagonal of a rectangular prism:d=l2+w2+h2 d = \sqrt{l^2 + w^2 + h^2} d=l2+w2+h2​where l l l, w w w, and h h h are the length, width, and height of the prism, respectively.

STEP 4

Substitute the given dimensions into the formula:d=402+402+302 d = \sqrt{40^2 + 40^2 + 30^2} d=402+402+302​

STEP 5

Calculate the length of the space diagonal:d=402+402+302 d = \sqrt{40^2 + 40^2 + 30^2} d=402+402+302​ =1600+1600+900 = \sqrt{1600 + 1600 + 900} =1600+1600+900​ =4100 = \sqrt{4100} =4100​ ≈64.03 \approx 64.03 ≈64.03

STEP 6

Round the result to the nearest centimeter:d≈64 cm d \approx 64 \, \text{cm} d≈64cm The length of the space diagonal is:64 cm \boxed{64 \, \text{cm}} 64cm​

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1. The box is a rectangular prism with dimensions $40 \, \text{cm} \times 40 \, \text{cm} \times 30 \, \text{cm}$ .
2. The space diagonal is the longest diagonal that runs from one corner of the box to the opposite corner.

1. Recall the formula for the space diagonal of a rectangular prism.
2. Substitute the given dimensions into the formula.
3. Calculate the length of the space diagonal.
4. Round the result to the nearest centimeter.

Recall the formula for the space diagonal of a rectangular prism:
$d = \sqrt{l^2 + w^2 + h^2}$
where $l$ , $w$ , and $h$ are the length, width, and height of the prism, respectively.

Substitute the given dimensions into the formula:
$d = \sqrt{40^2 + 40^2 + 30^2}$

Calculate the length of the space diagonal:
$d = \sqrt{40^2 + 40^2 + 30^2}$ $= \sqrt{1600 + 1600 + 900}$ $= \sqrt{4100}$ $\approx 64.03$

Round the result to the nearest centimeter:
$d \approx 64 \, \text{cm}$
The length of the space diagonal is:
$\boxed{64 \, \text{cm}}$