Need help very fast please!

Question

Need help very fast please!

1.) The length, width, and height of a rectangular pyramid are multiplied by 1/2. Which of the following describes the effect on the volume?

A.) The volume is multiplied by 1/8.

B.) The volume is multiplied by 3/2.

C.) The volume is multiplied by 2.

D.) The volume is multiplied by 1/6.

2.) The radius and the height of the cylinder are multiplied by 1/3. What will be the effect on the volume of the cylinder?

A.) The volume is multiplied by 1/9.

B.) The volume is multiplied by 2/9.

C.) The volume is multiplied by 1/27.

D.) The volume is multiplied by 1/3.

Need help very quickly!

Answer 1

For the first volume problem involving the rectangular pyramid, the normal volume formula is V = 1/3 (l)(w)(h). Since all 3 dimensions are being multiplied by 1/2, this involves multiplying the original formula by (1/2)(1/2)(1/2) which, put together, is multiplying by 1/8, so the volume will be 1/8 of what it was with the original dimensions.

For the cylinder problem, the volume formula for a cylinder is V = (pi)r² h. Since "r" becomes 1/3r when it is multiplied by 1/3, the r² now becomes (1/3r)² which is 1/9r². By the same adjustment, the "h" now becomes 1/3 h, so the original formula now has a 1/9 ( from the r) and a 1/3 ( from the h) being multiplied, which is 1/27, so the original volume is now 1/27 of what it was with the original dimensions.