Find the surface area of a square pyramid with a base length of 11 cm and a slant height of 15 cm.
472 cm2
451 cm2***
781 cm2
330 cm2
Find the volume of a rectangular prism with the following dimensions:
Length = 5 mm
Base = 7 mm
Height = 3 mm
142 mm3 ***
105 mm3
126 mm3
130 mm3
Please
Surface area of a square pyramid usually just adds up the surface area of the 4 isosceles triangles, not including the base
one of them:
base = 11
hypotenuse = 15
height^2 + 5.5^2 = 15^2
height^2 = 194.75
height = √194.75
area of one of them = (1/2)(11)√194.75 = appr 76.754..
so 4 of them = 307.0162
which is none of your choices, so let's add on the base of 11^2 or 121 to get appr 428 cm^2
(none of your answers fit)
2nd question:
what is 5x7x3 ?????
To find the surface area of a square pyramid, we need to calculate the areas of the base and the lateral faces separately and then add them together.
First, let's find the area of the base. The base of a square pyramid is a square, so we can find its area by squaring the length of one side. In this case, the base length is given as 11 cm, so the area of the base is 11 cm x 11 cm = 121 cm².
Next, let's find the area of the lateral faces. The lateral faces of a square pyramid are triangles, and we can calculate their areas using the formula: (1/2) x base x height. The base of each lateral face is the base length of the pyramid, which is 11 cm. The slant height is given as 15 cm, and since the slant height is the height of the triangular face, we can use it directly in the formula. Therefore, the area of each lateral face is (1/2) x 11 cm x 15 cm = 82.5 cm².
Since a square pyramid has four equal lateral faces, the total area of the lateral faces is 4 x 82.5 cm² = 330 cm².
Finally, to find the surface area of the square pyramid, we add the area of the base and the area of the lateral faces: 121 cm² + 330 cm² = 451 cm².
Therefore, the correct answer is 451 cm².
Now, let's move on to finding the volume of a rectangular prism.
To find the volume of a rectangular prism, we need to multiply the length, base, and height of the prism.
In this case, the length is given as 5 mm, the base is given as 7 mm, and the height is given as 3 mm.
To find the volume, we multiply these three dimensions together: 5 mm x 7 mm x 3 mm = 105 mm³.
Therefore, the correct answer is 105 mm³.