Chapter 7: Q19. (page 460)

GEOMETRY Use the formula $V = π r^{2} h$ to find the volume of the cylinder.

Short Answer

Expert verified

The volume of cylinder is $45 π x^{4}$ .

Step by step solution

Step 1. Replace the variables with their values.

Replace r with 3x and h with $5 x^{2}$ into $V = π r^{2} h$ .

$V = π {(3 x)}^{2} (5 x^{2})$

Step 2. Group the coefficients and the variables.

Group the coefficients and variables in the given expression.

$V = (π \cdot 3^{2} \cdot 5) (x^{2} \cdot x^{2})$

Step 3. Write the property of product of powers.

For any real number a and any integers m and n, $a^{m} \cdot a^{n} = a^{m + n}$ .

Step 4. Apply property of product of powers and simplify.

Apply the property of product of powers to the expression obtained in step 2 and simplify.

$V = (π \cdot 3^{2} \cdot 5) (x^{2 + 2}) = 45 π x^{4}$

Therefore, volume of cylinder is $45 π x^{4}$ .

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Equation	Related Expression	Power of ‘x’	Linear or non linear
$y = x$
$y = x^{2}$
$y = x^{3}$

GEOMETRY Use the formula $V = π r^{2} h$ to find the volume of the cylinder.

Short Answer

Step by step solution

Step 1. Replace the variables with their values.

Step 2. Group the coefficients and the variables.

Step 3. Write the property of product of powers.

Step 4. Apply property of product of powers and simplify.

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GEOMETRY Use the formulaV=πr2h to find the volume of the cylinder.

Short Answer

Step by step solution

Step 1. Replace the variables with their values.

Step 2. Group the coefficients and the variables.

Step 3. Write the property of product of powers.

Step 4. Apply property of product of powers and simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Applied Mathematics

Geometry

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

GEOMETRY Use the formula $V = π r^{2} h$ to find the volume of the cylinder.