Answer:
Part A
Cone
(where r is the radius and h is the height)
Given:
Hemisphere
Given
Therefore
volume of cone with radius a = volume of hemisphere with radius a
Part B
Take log of base 10:
Using log law
:
Using low law
Log tables
The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.
The mantissa is found using the log tables and is always prefixed by a decimal point.
The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number
Use the log tables to find
:
6.82 = 6.82 × 10⁰
⇒ characteristic = 0
log table: row 68, column 2 ⇒ mantissa 8338 ⇒ 0.8338
characteristic + mantissa = 0 + 0.8338 = 0.8338
Therefore,
Use the log tables to find
:
⇒ characteristic = -3
log table: row 50, column 0 ⇒ mantissa 6990 ⇒ 0.6990
characteristic + mantissa = -3 + 0.6990 = -2.301
Therefore,
Therefore,
Therefore,
Using