_________________________________

1. Use a formula to find the surface area of the square pyramid. (H.6ft.)(W.3ft.)(L.3ft.)

A. 45 ft
B. 81 ft***
C. 36 ft
D. 72 ft
_________________________________
2. Find the lateral area of the pyramid to the nearest whole unit. (H.22)(W.8)(L.8)

A. 176 m
B. 352 m
C. 704 m
D. 416 m***
_________________________________
3. Find the surface area of the cone to the nearest whole unit. (H.7in)(D.8in)

A. 226 in
B. 88 in
C. 377 in
D. 138 in***
_________________________________
4. Find the lateral area of the cone. Use 3.14 for pi and round to the nearest whole unit. (R.15cm)(H. 7 in)

A. 1,319 cm
B. 2,639 cm***
C. 707 cm
D. 2,026 cm
_________________________________
Thank You

1. 45 ftΒ²

2. 352 ftΒ²
3. 138 inΒ²
4. 1,319 cmΒ²
100% right βœ… I just took the test

stream tarzan and milo x toon

A.

B.
D.
A.

@Don't bother me and @yoyo are correct! 4/4

To find the answers to these questions, we need to use the formulas for finding the surface area and lateral area of different shapes. Let's go through each question one by one.

1. Surface area of a square pyramid:
The formula for finding the surface area of a square pyramid is:
Surface Area = Base Area + 4 * (0.5 * base width * slant height)

In this case, the base width and length are both 3ft, and the slant height is 6ft. Plugging these values into the formula, we get:
Surface Area = (3ft * 3ft) + 4 * (0.5 * 3ft * 6ft)
Surface Area = 9ft^2 + 4 * 9ft^2
Surface Area = 9ft^2 + 36ft^2
Surface Area = 45ft^2

So, the answer to the first question is option B. 81ft is incorrect.

2. Lateral area of a pyramid:
The formula for finding the lateral area of a pyramid is:
Lateral Area = (0.5 * perimeter of base) * slant height

In this case, the height and slant height of the pyramid are both 22m, and the width and length of the base are both 8m. To find the perimeter of the base, we add up all four sides:
Perimeter of base = 8m + 8m + 8m + 8m
Perimeter of base = 32m

Plugging these values into the formula, we get:
Lateral Area = (0.5 * 32m) * 22m
Lateral Area = 16m * 22m
Lateral Area = 352m^2

So, the answer to the second question is option D. 416m is incorrect.

3. Surface area of a cone:
The formula for finding the surface area of a cone is:
Surface Area = Ο€ * r * (r + slant height)

In this case, the height of the cone is 7in and the diameter is 8in, which means the radius is half of the diameter, so it is 4in. The slant height can be found using the Pythagorean theorem:
slant height = √(radius^2 + height^2)
slant height = √(4in^2 + 7in^2)
slant height = √(16in^2 + 49in^2)
slant height = √(65in^2)
slant height β‰ˆ 8.06in

Plugging these values into the formula, we get:
Surface Area = 3.14 * 4in * (4in + 8.06in)
Surface Area = 3.14 * 4in * 12.06in
Surface Area β‰ˆ 151.62in^2

Rounding to the nearest whole unit, the answer to the third question is D. 138in is incorrect.

4. Lateral area of a cone:
The formula for finding the lateral area of a cone is:
Lateral Area = Ο€ * r * slant height

In this case, the radius is 15cm and the height is 7in. Converting the height to cm, we get 17.78cm. The slant height can be found using the Pythagorean theorem:
slant height = √(radius^2 + height^2)
slant height = √(15cm^2 + 17.78cm^2)
slant height = √(225cm^2 + 316.48cm^2)
slant height = √(541.48cm^2)
slant height β‰ˆ 23.26cm

Plugging these values into the formula, we get:
Lateral Area = 3.14 * 15cm * 23.26cm
Lateral Area β‰ˆ 1081.59cm^2

Rounding to the nearest whole unit, the answer to the fourth question is B. 2,639cm is incorrect.

So, to recap the correct answers:
1. A. 45ft
2. D. 416m
3. D. 138in
4. B. 2,639cm

If the pyramid has base of side w and height h, then each lateral face of the pyramid is a triangle with base = w, and height equal to the slant height:

√(h^2 + (w/2)^2)

similarly, the lateral area of a cone of height h and radius r is
Ο€rs = Ο€r√(r^2+h^2)

so plug in your numbers