Math Problem Statement

次の立体の体積と表面積を求めなさい。 (1) 四角柱 (2) 円柱

Solution

This image contains two 3D shapes: a rectangular prism and a cylinder. It looks like you are asked to calculate the volume and surface area of each shape.

  1. Rectangular Prism (四角柱):

    • Dimensions: Length = 6 cm, Width = 3 cm, Height = 5 cm
    • Volume of a rectangular prism: V=Length×Width×HeightV = \text{Length} \times \text{Width} \times \text{Height}
    • Surface area of a rectangular prism: A=2lw+2lh+2whA = 2lw + 2lh + 2wh
  2. Cylinder (円柱):

    • Dimensions: Radius = 5 cm, Height = 10 cm
    • Volume of a cylinder: V=πr2hV = \pi r^2 h
    • Surface area of a cylinder: A=2πr2+2πrhA = 2\pi r^2 + 2\pi rh

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Math Problem Analysis

Mathematical Concepts

Volume of Rectangular Prism
Surface Area of Rectangular Prism
Volume of Cylinder
Surface Area of Cylinder

Formulas

Volume of Rectangular Prism: V = Length × Width × Height
Surface Area of Rectangular Prism: A = 2lw + 2lh + 2wh
Volume of Cylinder: V = πr^2h
Surface Area of Cylinder: A = 2πr^2 + 2πrh

Theorems

Volume and Surface Area of 3D Shapes

Suitable Grade Level

Grades 7-9