Part 1) <span>If a cylinder has a surface area of 36 square inches and its radius is 1.6 inches, how tall is the cylinder in inches? π = 3.14. Round to the nearest tenth.
we know that surface area of the cylinder=2*area of the base+perimeter of the base*height
area of the base==pi*r</span>²*h-----> 3.14*1.6²*h----> 8.0384*h in²
perimeter of the base=2*pi*r---> 2*3.14*1.6----> 10.048 in
surface area=36 in² so 36=2*[8.0384*h]+10.048*h----> 36=26.1248*h h=36/26.1248----> h=1.38 in------> h=1.4 in
the answer Part 1) is h=1.4 in
Part 2) <span>2. A regular hexagonal pyramid has a base area of 29 in^2 and a lateral area of 210 in^2. What is the surface area of the hexagonal pyramid?
surface area of the hexagonal pyramid=2*area of base+lateral area </span>surface area of the hexagonal pyramid=2*29+210----> 268 in²
the answer part 2) is surface area=268 in²
Part 3)<span> What is the surface area of the following cylinder in square inches? Use π = 3.14 and round your answer to the nearest tenth. Radius = 3.2 Height = 4.1 </span>we know that surface area of the cylinder=2*area of the base+perimeter of the base*height
area of the base==pi*r²*h-----> 3.14*3.2²*4.1----> 131.83 in²
perimeter of the base=2*pi*r---> 2*3.14*3.2----> 20.096in
part 4)<span>A cube has surface area of 150 in^2. How long is each side of the cube?
we know that surface area of cube=6*b</span>² where b is the length side of the cube SA=6*b²------> b=√SA/6------> b=√150/6-----> √25----> b=5 in
the answer Part 4) is b=5 in
Part 5) <span>A cube has sides that are 3 in. long. What is the surface area of the cube? </span>we know that surface area of cube=6*b² where b is the length side of the cube b=3 in so SA=6*3²----> 54 in²
the answer Part 5) is SA=54 in²
Part 6) <span>What is the surface area of this box? Height = 3.5 Length = 6 width = 3
surface area of the box=2*area of the base+perimeter of base*height
area of the base=6*3----> 18 ft</span>²
perimeter of the base=2*[6+3]----> 18 ft height=3.5 ft
surface area of the box=2*18+18*3.5----> 99 ft²
the answer Part 6) is SA=99 ft²
Part 7) <span>If a cylinder has a surface area of 59 square inches and its radius is 2.1 inches, how tall is the cylinder in inches? Use π = 3.14. Round to the nearest tenth </span>
we know that surface area of the cylinder=2*area of the base+perimeter of the base*height
area of the base==pi*r²*h-----> 3.14*2.1²*h----> 13.8474*h in²
perimeter of the base=2*pi*r---> 2*3.14*2.1----> 13.188 in
surface area=59 in² so 59=2*[13.8474*h]+13.188*h----> 59=40.8828*h h=59/40.8828----> h=1.44 in------> h=1.4 in
the answer Part 7) is h=1.4 in
Part 8) <span>What is the surface area of the cone below, rounded to the nearest tenth? Use π = 3.14. Height = 12 Radius = 5 surface area of the cone=pi*r</span>²+pi*r*l r=5 in h=12 in l=slant height l²=r²+h²----> l²=5²+12²----> l²=169-----> l=13 in
surface area of the cone=3.14*5²+3.14*5*13-----> 282.6 in²
the answer Part 8) is SA=282.6 in²
Part 9) <span>A square pyramid has a surface area of 202 ft^2 and a base area of 53 ft^2. What is the lateral area of the pyramid?
we know that surface area=area of the base+lateral area lateral area=surface area-area of the base lateral area=202-53----> 149 ft</span>²
the answer Part 9) is LA=149 ft²
Part 10)<span>What is the surface area of the cone below, rounded to the nearest tenth? Use π = 3.14 Radius = 2 Height = 4 </span> surface area of the cone=pi*r²+pi*r*l r=2 cm h=4 cm l=slant height l²=r²+h²----> l²=2²+4²----> l²=20-----> l=4.47 cm
surface area of the cone=3.14*2²+3.14*2*4.47-----> 40.63 cm²
