A corner is sawn off a cuboidal wooden block with one straight cut. The piece removed is a pyramid whose base is a right-angled triangle with legs 6 cm and 5 cm, and whose apex stands 3 cm directly above the corner where those legs meet. Find the volume of the piece removed in cm³.

Question

Accepted Answer

15. Base area = ½ × 6 × 5 = 15 cm². For a pyramid, volume = (1/3) × base area × height = (1/3) × 15 × 3 = 15 cm³. (Treating the piece as a whole cuboid would wrongly give 6 × 5 × 3 = 90 cm³.)

A corner is sawn off a cuboidal wooden block with one straight cut. The piece removed is a pyramid whose base is a right-angled triangle with legs 6 cm and 5 cm, and whose apex stands 3 cm directly above the corner where those legs meet. Find the volume of the piece removed in $cm^{3}$ .

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More Areas & Volumes practice

A corner is sawn off a cuboidal wooden block with one straight cut. The piece removed is a pyramid whose base is a right-angled triangle with legs 6 cm and 5 cm, and whose apex stands 3 cm directly above the corner where those legs meet. Find the volume of the piece removed in cm3.

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Areas & Volumes practice

A corner is sawn off a cuboidal wooden block with one straight cut. The piece removed is a pyramid whose base is a right-angled triangle with legs 6 cm and 5 cm, and whose apex stands 3 cm directly above the corner where those legs meet. Find the volume of the piece removed in $cm^{3}$ .