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:
[tex]LA=4s^2[/tex]
We have s = 4.1 ft.
Substitute:
[tex]LA=4(4.1^2)=4(16.81)=67.24\ ft^2[/tex]
Q4.
The formula of a surface area if a cylinder:
[tex]SA=2\pi r^2+2\pi rH[/tex]
r - radius
H - height
We have 2r = 62 cm → r = 31 cm, H = 85 cm.
Substitute:
[tex]SA=2\pi(31^2)+2\pi(31)(85)=2\pi(961)+5270\pi=1922\pi+5270\pi=7192\pi\ cm^2[/tex]
[tex]\pi\approx3.14\to SA\approx(7192)(3.14)=22582.88\ cm^2[/tex]
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:
[tex]A=s^2[/tex]
The formula of an area of a triangle with base b and height h:
[tex]A=\dfrac{bh}{2}[/tex]
We have s = 5 cm, b = s = 5 cm, h = 9 cm.
Substitute:
[tex]A_{\square}=5^2=25\ cm^2\\\\A_{\triangle}=\dfrac{(5)(9)}{2}=\dfrac{45}{2}=22.5\ cm^2[/tex]
The surface area:
[tex]SA=A_{\square}+4A_{\triangle}\\\\SA=25+4(22.5)=25+90=115\ cm^2[/tex]
Q10.
The lateral sides are two pairs of rectangles.
The formula of an area of a rectangle:
[tex]A=l\cdot w[/tex]
l - length
w - width
We have the rectangles:
5 in × 10 in and 7 in × 10 in
Substitute:
[tex]A_1=(5)(10)=50\ in^2\\\\A_2=(7)(10)=70\ in^2[/tex]
The lateral area:
[tex]LA=2A_1+2A_2\\\\LA=2(50)+2(70)=100+140=240\ in^2[/tex]
