Question

50 Points thanks for the help :)

Answer 1

Answer:

Q3. 67.24 sq. ft.

Q4. 22582.88 sq. cm.

Q6. 115 sq. cm.

Q10. 240 sq. in.

Step-by-step explanation:

Q3.

The formula of a lateral area of a cube with side s:

$LA=4s^2$

We have s = 4.1 ft.

Substitute:

$LA=4(4.1^2)=4(16.81)=67.24\ ft^2$

Q4.

The formula of a surface area if a cylinder:

$SA=2\pi r^2+2\pi rH$

r - radius

H - height

We have 2r = 62 cm → r = 31 cm, H = 85 cm.

Substitute:

$SA=2\pi(31^2)+2\pi(31)(85)=2\pi(961)+5270\pi=1922\pi+5270\pi=7192\pi\ cm^2$

$\pi\approx3.14\to SA\approx(7192)(3.14)=22582.88\ cm^2$

Q6.

The surface area of a square piramid is

base - square

lateral sides - four triangles

The formula of an area of a square with sides s:

$A=s^2$

The formula of an area of a triangle with base b and height h:

$A=\dfrac{bh}{2}$

We have s = 5 cm, b = s = 5 cm, h = 9 cm.

Substitute:

$A_{\square}=5^2=25\ cm^2\\\\A_{\triangle}=\dfrac{(5)(9)}{2}=\dfrac{45}{2}=22.5\ cm^2$

The surface area:

$SA=A_{\square}+4A_{\triangle}\\\\SA=25+4(22.5)=25+90=115\ cm^2$

Q10.

The lateral sides are two pairs of rectangles.

The formula of an area of a rectangle:

$A=l\cdot w$

l - length

w - width

We have the rectangles:

5 in × 10 in and 7 in × 10 in

Substitute:

$A_1=(5)(10)=50\ in^2\\\\A_2=(7)(10)=70\ in^2$

The lateral area:

$LA=2A_1+2A_2\\\\LA=2(50)+2(70)=100+140=240\ in^2$