>> Elementary Mathematics >> Volume and surface area

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- Volume and surface area

1). If the total surface area of a cube is 6 sq units, then what is the volume of the cube?
Total surface area of a cube = 6 \( \Large a^{2} \) => 6 = 6 \( \Large a^{2} \) = \( \Large a^{2} \) = 1 Therefore, a = 1 Now, volume of the cube = \( \Large a^{3} \) = \( \Large 1^{3} \) = 1 cu unit | ||||

2). If the volume of a cube is 729 cu. cm. what is the length of its diagonal?
Volume of cube = \( \Large Side^{3} \) Therefore, 729 = \( \Large a^{3} \) => a = 9 cm Therefore, Diagonal of cube = \( \Large Side \times \sqrt{3} \) \( \Large 9 \times \sqrt{3} \) \( \Large 9\sqrt{3} \) cm . | ||||

3). Find the surface area of a cuboid 10 m long, 5 In broad and 3 m high.
Given that, l = 10 m, b = 5m, h = 3m | ||||

4). The surface area of a cube is 726 sq cm. Find the volume of the cube.
According to the question, | ||||

5). The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm x 6cm x 2 cm, is
Length of largest pencil that can be kept in a box | ||||

6). Internal length, breadth and height of a rectangular box are 10 cm, 8 cm and 6 cm, respectively. How many boxes are needed which can be packed in a cube whose volume is 6240 cu. cm.?
Volume of rectangular box | ||||

7). A cube has each edge 2 cm and a cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a certain container is sufficient to paint an area equal to 54 \( \Large cm^{2} \). Which one of the following is correct?
Surface area of cube which can be painted = \( \Large 6 \left(Side\right)^{2} = 6 \left(2\right)^{2} = 2 cm^{2} \) | ||||

8). The whole surface area of a rectangular block is 8788 sq cm. If length, breadth and height are in the ratio of 4 : 3 : 2, then find the length.
Let length. breadth and height be 4x, 3x and 2x respectively. Whole surface area = \( \Large 2 \left(lb+bh+lh\right) \) => \( \Large \left(lb+bh+lh\right) = \frac{8788}{2} = 4394 \) \( \Large \left(4 \times 3 + 3 \times 2 + 2 \times 4\right)x^{2} = 4394 \) => \( \Large 26x^{2} = 4397 \) => \( \Large x^{2} = 169 => x = 13 \) Therefore, Length = \( \Large 4x = 4 \times 13 = 52 cm \) | ||||

9). What are the dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cu cm, surface area 484 sq cm and the area of the base 72 sq cm?
Volume of the cuboid = \( \Large 720 cm^{3} \) | ||||

10). The volume of a cube is equal to sum of its edges. What is the total surface area in square units?
Let the edge of a square be x and sum of its edges =12x |