What is the surface area of the regular pyramid? What is the surface area of a square pyramid with a height of 10.4 m and a base side length of 12.4 m? a. 141.4 cm c. 167.4 m b. 162.4 cm d. 188.4 cm
Find the volume and the lateral area of a frustum of a right circular cone whose radii are 4 and 8 cm, and slant height is 6 cm. Lateral area = Total surface area - area of base - area of top
Find the volume and the lateral area of a frustum of a right circular cone whose radii are 4 and 8 cm, and slant height is 6 cm. Lateral area = Total surface area - area of base - area of top
Part 1) 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*r²*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) 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 surface area of the hexagonal pyramid=2*29+210> 268 in²
the answer part 2) is surface area=268 in²
Part 3) 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 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)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*b² 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) A cube has sides that are 3 in. long. What is the surface area of the cube? 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) 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 ft²
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) 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
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) 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*r²+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) 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 ft²
the answer Part 9) is LA=149 ft²
Part 10)What is the surface area of the cone below, rounded to the nearest tenth? Use π = 3.14 Radius = 2 Height = 4
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
Part 1) 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*r²*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) 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 surface area of the hexagonal pyramid=2*29+210> 268 in²
the answer part 2) is surface area=268 in²
Part 3) 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 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)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*b² 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) A cube has sides that are 3 in. long. What is the surface area of the cube? 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) 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 ft²
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) 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
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) 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*r²+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) 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 ft²
the answer Part 9) is LA=149 ft²
Part 10)What is the surface area of the cone below, rounded to the nearest tenth? Use π = 3.14 Radius = 2 Height = 4
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
Q1) the lateral area of the pyramid is the total area of all the lateral faces excluding the base. In this regular octagonal pyramid, the lateral sides are triangles. As there are 8 triangles we need to find the area of all 8 sides. Area of one lateral triangle face = 1/2 * base * slant height slant height is the hypotenuse of the right angled triangle formed from the base of the pyramid with the perpendicular height. slant height - l l² = 7² + 7² = 49 *2 l² = 98 l = √98 l = 9.9 Area = 1/2 * 5.8 cm * 9.9 cm = 28.71 cm² There are 8 sides total lateral area = 8 * 28.71 = 229.68 rounded off is 229.7 cm² third option is correct - 229.7 cm²
Q2) in the triangular face, the lateral edge makes a 60° angle with the base edge. Therefore 2 of the angles are 60° each, since the sum of the interior angles of a triangle is 180°, the third angle too is 60°. this makes the triangle an equilateral triangle with equal angles, hence equal sides. since lateral edge is 8 cm,base edge too is 8 cm. since this is an equilateral triangle, the perpendicular line cuts the base edge at its midpoint, bisecting the line forming 2 right angled triangles. in the right angled triangle, height of triangle is x slant height , base = 8 /2 = 4 cm hypotenuse = 8 cm We need to find x, use Pythogoras' theorem 4² + x² = 8² 16 + x² = 64 x² = 62 - 16 x = √48 x = √4x√4x√3 = 2x2√3 = 4√3 cm
Q3) surface area of the square pyramid surface area of the base + surface area of triangular faces square area = length x length = 6.2 x 6.2 = 38.44 yd² triangular face area = 1/2 * length * height since the angle between lateral edge and base edge is 60°, its an equilateral triangle where all sides are equal. in this case each side is 6.2 yd. to find the perpendicular height, use pythogoras' theorem the perpendicular line(slant height ) cuts the base edge at its midpoint, therefore length of the right angled triangle is = 6.2/2 = 3.1 yd
slant height - l l² + 3.1² = 6.2² l² = 38.44 -9.61 l² = 28.83 l = 5.37 area = 1/2 *length *height = 1/2 * 6.2 * 5.37 = 16.64 yd² there are 4 triangles = 4 * 16.64 = 66.58 yd² total area = 38.44 + 66.58 = 105 yd² correct answer is 3rd option - 105 yd²
Q1) the lateral area of the pyramid is the total area of all the lateral faces excluding the base. In this regular octagonal pyramid, the lateral sides are triangles. As there are 8 triangles we need to find the area of all 8 sides. Area of one lateral triangle face = 1/2 * base * slant height slant height is the hypotenuse of the right angled triangle formed from the base of the pyramid with the perpendicular height. slant height - l l² = 7² + 7² = 49 *2 l² = 98 l = √98 l = 9.9 Area = 1/2 * 5.8 cm * 9.9 cm = 28.71 cm² There are 8 sides total lateral area = 8 * 28.71 = 229.68 rounded off is 229.7 cm² third option is correct - 229.7 cm²
Q2) in the triangular face, the lateral edge makes a 60° angle with the base edge. Therefore 2 of the angles are 60° each, since the sum of the interior angles of a triangle is 180°, the third angle too is 60°. this makes the triangle an equilateral triangle with equal angles, hence equal sides. since lateral edge is 8 cm,base edge too is 8 cm. since this is an equilateral triangle, the perpendicular line cuts the base edge at its midpoint, bisecting the line forming 2 right angled triangles. in the right angled triangle, height of triangle is x slant height , base = 8 /2 = 4 cm hypotenuse = 8 cm We need to find x, use Pythogoras' theorem 4² + x² = 8² 16 + x² = 64 x² = 62 - 16 x = √48 x = √4x√4x√3 = 2x2√3 = 4√3 cm
Q3) surface area of the square pyramid surface area of the base + surface area of triangular faces square area = length x length = 6.2 x 6.2 = 38.44 yd² triangular face area = 1/2 * length * height since the angle between lateral edge and base edge is 60°, its an equilateral triangle where all sides are equal. in this case each side is 6.2 yd. to find the perpendicular height, use pythogoras' theorem the perpendicular line(slant height ) cuts the base edge at its midpoint, therefore length of the right angled triangle is = 6.2/2 = 3.1 yd
slant height - l l² + 3.1² = 6.2² l² = 38.44 -9.61 l² = 28.83 l = 5.37 area = 1/2 *length *height = 1/2 * 6.2 * 5.37 = 16.64 yd² there are 4 triangles = 4 * 16.64 = 66.58 yd² total area = 38.44 + 66.58 = 105 yd² correct answer is 3rd option - 105 yd²
4
Get Answer
14
