Posted by **Kayla** on Thursday, March 8, 2012 at 12:45pm.

A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

- geometry -
**Steve**, Thursday, March 8, 2012 at 3:22pm
the actual values of the dimensions make no difference.

If the original base sides are s, the height is h, then the volume v is

v = 1/3 s^2 * h

now, multiply each dimension by 5 and your new volume V is

V = 1/3 (5s)^2 * (5h)

= 1/3 * 25s^2 * 5h

= 125 * 1/3 s^2 * h

= 125v

or, 5^3 * v

scaling the dimensions of a figure by a factor of n means

area is scaled by n^2

volume is scaled by n^3

## Answer This Question

## Related Questions

- math - A wooden pyramid, 12 inches tall, has a square base. A carpenter ...
- Mathematics - OPQRS is a right pyramid whose base is a square of sides 12cm each...
- alegebra1 - The base edge of a square pyramid is 30 cm. The pyramid is 6 cm ...
- Maths - OPQRS is a right pyramid whose base is a square of sides 12cm each. ...
- Maths - OPQRS is a right pyramid whose base is a square of sides 12cm each. ...
- Geometry - A Pyramid has a height of 6cm and base edge 8cm. A similar pyramid ...
- math - a square based pyramid has a volume of 1100 mm cubed its height is 15 mm ...
- geometry - The base of a pyramid is a square. The perimeter of the base is 20ft...
- MATH - A GREAT PYRAMID HAS A SQUARE BASE 230M ON EACH SIDE. THE 4 TRIANGULAR ...
- MATH - E LARGEST PYRAMID IN THE U.S. IS THE LUXUR HOTEL IN VEGAS. THE VOLUME OF ...

More Related Questions