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2 years ago

A Crayon is shown here.

Mathematics

1 answer:

Aleks04 [339]2 years ago

3 0

The volume of the single crayon is 89.5 cm³, then the total volume of the crayons will be 2148 cm³. Then the correct option is D.

<h3>What is Geometry?</h3>

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A Crayon is shown here.

There are 24 crayons in a box.

The approximate total volume of the crayons will be

Total Volume of crayons = 24 × volume of the single crayon

The crayon is the combination of the cone and the cylinder

Then the volume of the single crayon (V₁) will be

$\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times r^2 \times h \right ) + \left ( \pi \times r^2 \times h \right )\\\\\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times 1.5^2 \times 2 \right ) + \left ( \pi \times 1.5^2 \times 12 \right )\\\\V_1 = 4.712 + 84.82\\\\V_1 = 89.535 \approx 89.5$

Then the Total volume will be

Total volume = 24 × 89.5

Total volume = 2148 cm³

More about the geometry link is given below.

brainly.com/question/7558603

#SPJ1

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Match the numerical expressions to their simplified forms

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Answer:

$1.\ \ p^2q = (\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}$

$2.\ \ pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

$3.\ \ pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$4.\ \ p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

Step-by-step explanation:

Required

Match each expression to their simplified form

$(\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$(\frac{p^{5-(-3)}}{q^{-4}})^{\frac{1}{4}}$

$(\frac{p^{5+3}}{q^{-4}})^{\frac{1}{4}}$

$(\frac{p^8}{q^{-4}})^{\frac{1}{4}}$

Split the fraction in the bracket

$(p^8*\frac{1}{q^{-4}})^{\frac{1}{4}}$

Simplify the fraction by using the following law of indices;

$\frac{1}{a^{-m}} = a^m$

The expression becomes

$(p^8*q^4)^{\frac{1}{4}}$

Further simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

$(p^{8*\frac{1}{4}}\ *\ q^4*^{\frac{1}{4}})$

$(p^{\frac{8}{4}}\ *\ q^{\frac{4}{4}})$

$p^2q$

Hence,

$(\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}} = p^2q$

$(\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$({p^2q^{7-4}}})^{\frac{1}{2}}$

$({p^2q^3}})^{\frac{1}{2}}$

Further simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

${p^{2*\frac{1}{2}}q^{3*\frac{1}{2}}}}$

$pq^{\frac{3}{2}}}$

Hence,

$pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

$\frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

Simplify the numerator as thus:

$\frac{p^{\frac{1}{2}} * q^3*^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{(pq)^{\frac{-1}{2}}}$

Simplify the denominator as thus:

$\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{p^{\frac{-1}{2}}q^{\frac{-1}{2}}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$p^{\frac{1}{2} - (\frac{-1}{2} )} * q^{\frac{3}{2} - (\frac{-1}{2}) }$

$p^{\frac{1}{2} +\frac{1}{2} } * q^{\frac{3}{2} + \frac{1}{2} }$

$p^{\frac{1+1}{2}} * q^{\frac{3+1}{2}}$

$p^{\frac{2}{2}} * q^{\frac{4}{2}}$

$pq^2$

Hence,

$pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$(p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

Simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

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$p^{\frac{6}{3}}\ *\ q^{\frac{3*1}{2*3}}$

$p^2 *\ q^{\frac{3}{6}}$

$p^2 *\ q^{\frac{1}{2}$

$p^2q^{\frac{1}{2}$

Hence

$p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

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