Question

This figure represents a small weight that is to be covered on all sides with a floral fabric. How much fabric is needed to cover the weight? Enter your answer as a decimal in the box.​

Answer 1

Total surface area of Cuboid:

If
`$l$` be the length of cuboid,
`$b$` be the breadth of cuboid and
`$h$` be the height of cuboid, then its total surface area (TSA) of cuboid is given by,

`\;\longrightarrow\boxed{\tt{TSA = 2(lb + bh + lh)}}`

A cuboid is also known as rectangular prism.

Elucidation:

We need to find the surface area of the cuboid or rectangular prism whose length, breadth and height are given.

• Length = 6 1/2 = 6.5cm
• Breadth = 2 1/2 = 2.5cm
• Height = 2 2/2 = 2.5cm

Now by using the formula of surface area nd substituting the given values, we get the following results:

`\implies\tt{Surface\;area = 2(6.5 * 2.5 + 2.5 * 2.5 + 6.5 * 2.5)}\\`

`\implies\tt{Surface\;area = 2(16.25 + 6.25 + 16.25)}\\`

`\implies\tt{Surface\;area = 2(38.75)}\\`

`\implies\boxed{\pmb{\tt{Surface\;area = 77.5}}}\\`

Hence, this is our required solution for this question.

`\rule{300}{1}`

Additional information:

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²
• Volume of cuboid = l * b * h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of sphere = 4/3πr³
• Surface area of sphere = 4πr²
• Volume of hemisphere = ⅔ πr³
• C.S.A of hemisphere = 2πr²
• T.S.A of hemisphere = 3πr²

Answer 2

77.5 cm²

Explanation:

We need to find the surface area of the rectangular prism.

Total surface area = 2(lw + wh + lh)

where:

• l = length of base
• w = width of base
• h = height of prism

Given dimensions:

`\textsf{length}=\sf 6\frac12\:cm=6.5\:cm`

`\textsf{width}=\sf 2\frac12\:cm=2.5\:cm`

`\textsf{height}=\sf 2\frac12\:cm=2.5\:cm`

Substituting these value into the formula:

`\begin{aligned}\textsf{Surface area} & =\sf 2(6.5 \cdot 2.5+2.5 \cdot 2.5+6.5 \cdot 2.5)\\ & = \sf2(16.25+6.25+16.25)\\ & = \sf 2(38.75)\\ & =\sf77.5\:cm^2 \end{aligned}`

Therefore, 77.5 cm² of fabric is needed to cover the weight.