Question

Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.

Which is the slant height of the pyramid if Helen uses all the clay?


a.3 inches
b.4 inches
c.5 inches
d.6 inches

Answer 1

Well if you plug in those values into an equation and a drawing and measure it (which I'm doing right now) you can find your answer. 3 inches is wrong because it is too small to connect with the base and the tip of the pyramid (you can also plug these into a pyramid calculator [which I'm also doing]) 4 inches is also too short for the base and the tip. 6 inches is too long. Your answer is 5 inches. it matches up in the calculator and my graphs.



Hoped I helped!

Answer 2

option c is correct

slant height of the pyramid is, 5 inches

Explanation:

Volume of a pyramid(V) is given by:

`V = (1)/(3) \cdot B \cdot h`

where,

B is the base area

h is the height.

As per the statement:

Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.

Since, base is square

⇒Base area =
`(side)^2`

⇒ Base area =
`6^2 = 36` square inches.

and

volume of solid square right pyramid(V)= 48 cubic inches

Substitute these we have;

`48 = (1)/(3) \cdot 36 \cdot h`

⇒
`48 = 12h`

Divide both sides by 12 we have;

`h = 4` inches.

To find the slant height:

Using Pythagoras theorem.

`l^2 = h^2+(b^2)/(4)`

where

l is the slant height

b is the base edge of the pyramid.

then;

`l^2 = 4^2+(36)/(4)`

⇒
`l^2 = 16+9 = 25`

⇒
`l = √(25) =5` inches

therefore, the slant height of the pyramid is, 5 inches