Solve the Problem $B$ And the Height $h$ Of a Pyramid Are Related to the Pyramid's Volume

question 420

Multiple Choice

Solve the problem.
-The area of the base $B$ and the height $h$ of a pyramid are related to the pyramid's volume $V$ by the formula $\mathrm { V } = \frac { 1 } { 3 } \mathrm { Bh }$ . How is $\mathrm { dV } / \mathrm { dt }$ related to $\mathrm { dh } / \mathrm { d }$ t if $\mathrm { B }$ is constant?

• A) \(\frac { \mathrm { dV } } { \mathrm { dt } } = \frac { \mathrm { B } } { 3 } \frac { \mathrm { dh } } { \mathrm { dt } }\)
• B) \(\frac { d V } { d t } = B \frac { d h } { d t }\)
• C) \(\frac { \mathrm { dV } } { \mathrm { dt } } = \frac { \mathrm { dh } } { \mathrm { dt } }\)
• D) \(\frac { \mathrm { dV } } { \mathrm { dt } } = \frac { 1 } { 3 } \frac { \mathrm { dh } } { \mathrm { dt } }\)

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Definitions:

Gross Private Domestic Investment

The total capital investment in an economy by private sector entities, excluding government spending.

Durable Goods

Goods not for immediate consumption that can be used over a period of time, such as appliances, cars, and furniture.

Business Inventories

The stocks of goods and materials that firms hold for the purpose of sale or input into production, often used to meet consumer demand or continue production.

Welfare Benefits

Financial assistance provided by the government to individuals or groups in need, aiming to support well-being and economic stability.