This problem asks for the total area of a composite figure consisting of a rectangle (10 cm × 4 cm) and a semicircle (diameter 4 cm), requiring the result in square centimeters. We need to find the area of each part separately and add them. Rectangle area: A₁ = 10 × 4 = 40 cm². Semicircle area: A₂ = ½π(2)² = ½π(4) = 2π cm² (radius = diameter/2 = 2 cm). Total area: A = 40 + 2π cm². A common error is calculating the full circle area instead of the semicircle, which would give 40 + 4π cm². Always check whether you need a full circle or semicircle in composite figures.

This problem asks for the area of a parallelogram with base 8 m and height 5 m, requiring the result in square meters. The formula for the area of a parallelogram is A = base × height, where the height is perpendicular to the base. Substituting the given values: A = 8 × 5 = 40 m². A common error is using the slant side length instead of the perpendicular height, which would give an incorrect result. Remember that for parallelograms, always use the perpendicular height, not the slanted side length.

This problem asks for the volume of a rectangular prism with dimensions 4 m × 5 m × 6 m, requiring the result in cubic meters. The formula for the volume of a rectangular prism is V = length × width × height. Substituting the given dimensions: V = 4 × 5 × 6 = 120 m³. A common error is adding the dimensions instead of multiplying them, which would incorrectly give 15 m. Remember that volume always involves multiplying all three dimensions for rectangular prisms.

This problem asks for the area of a triangle with base 10 m and height 8 m, requiring the result in square meters. The formula for the area of a triangle is A = ½bh, where b is the base and h is the height. Substituting the given values: A = ½(10)(8) = ½(80) = 40 m². A common error is forgetting the ½ factor, which would incorrectly give 80 m². Always remember that triangle area is exactly half the area of a rectangle with the same base and height.

This problem asks for the volume of a cylinder with radius 3 cm and height 10 cm, requiring the result in cubic centimeters. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Substituting the given values: V = π(3)²(10) = π(9)(10) = 90π cm³. A common error is confusing this with surface area formulas or forgetting to square the radius. Remember that cylinder volume combines the circular base area (πr²) with the height.

This problem asks for the area of a rectangle with length 12 cm and width 7 cm, requiring the result in square centimeters. The formula for the area of a rectangle is A = length × width. Substituting the given dimensions: A = 12 × 7 = 84 cm². A common error is adding the dimensions instead of multiplying them, which would give 19 cm (the perimeter calculation would be 2(12 + 7) = 38 cm). Always multiply length and width for area calculations.

This problem asks for the area of a circle with radius 6 cm, requiring the result in square centimeters. The formula for the area of a circle is A = πr², where r is the radius. Substituting the given radius: A = π(6)² = π(36) = 36π cm². A common error is confusing the area formula with the circumference formula (C = 2πr), which would give 12π. When working with circles, always remember that area involves r² while circumference involves r.

This problem asks for the area of a trapezoid with bases 10 cm and 14 cm and height 6 cm, requiring the result in square centimeters. The formula for the area of a trapezoid is A = ½h(b₁ + b₂), where h is the height and b₁, b₂ are the parallel bases. Substituting the given values: A = ½(6)(10 + 14) = ½(6)(24) = ½(144) = 72 cm². A common error is forgetting the ½ factor or adding the bases incorrectly. Remember that trapezoid area uses the average of the two bases multiplied by the height.

This problem asks for the volume of a sphere with radius 5 cm, requiring the result in cubic centimeters. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius. Substituting the given radius: V = (4/3)π(5)³ = (4/3)π(125) = (4 × 125π)/3 = 500π/3 cm³. A common error is using the surface area formula (4πr²) or forgetting the (4/3) coefficient. Remember that sphere volume involves r³ with the specific coefficient (4/3)π.

This problem asks for the volume of a cone with radius 4 cm and height 9 cm, requiring the result in cubic centimeters. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height. Substituting the given values: V = (1/3)π(4)²(9) = (1/3)π(16)(9) = (1/3)π(144) = 48π cm³. A common error is using the cylinder formula without the (1/3) factor, which would give 144π cm³. Remember that cone volume is exactly one-third of the corresponding cylinder volume.