All categories

3 years ago

Anne wants to fill 12 hanging baskets with compost. Each hanging basket is a hemisphere of diameter 40 cm.

Mathematics

1 answer:

murzikaleks [220]3 years ago

3 0

Answer:

Step-by-step explanation:

Steps to answering this question

determine the volume of the 12 basket

volume of a hemisphere = (2/3)πr^3

n = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

radius = 40/2 = 20 cm

volume of one hemisphere = (2/3) x (22/7) x (20^3) = 16,761.90 cm^3

volume of the 12 baskets = 16,761.90 cm^3 x 12 = 201,142.86 cm^

2. convert the litres of compost to cm and multiply by the total bags of compost

1 litre = 1000cm

1 bag of compost = 50 x 1000 = 50,000

4 bags of compost = 50,000 x 4 = 200,000 cm

3. compare which figure is higher. the figure gotten in step 1 or 2

201,142.86 cm^3 is greater than 200,000

there is no enough compost

473691.4

273691.4

You might be interested in

What is one-fourth of the circumference of a circle that measures 12 centimeters around?

emmainna [20.7K]

Answer:

Step-by-step explanation:

12cm / 4 = 3cm

5 0

3 years ago

A group of 14 and 15-year-olds were polled on their favorite season. The results are shown in the frequency table.

Yakvenalex [24]

Answer:

1. 4 categories are shown in the rows.

2. 2 categories are shown in the columns.

3. The number of 14 year olds that consider winter their favorite season is 12.

4. Total number of people polled is 82.

Step-by-step explanation:

The question is to test the ability of a student to group data using a frequency table accurately, and make appropriate deductions from it. Consider the attachment for the accurate table required to answer the given questions.

If the given information is grouped as required, thus the answers to the questions are:

i. 4 categories are shown in the rows.

ii. 2 categories are shown in the columns.

iii. The number of 14 year olds that considers winter their favorite season is 12.

iv. Total number of people polled is 82.

5 0

3 years ago

What can be multiplied to get 40 but also added to get 29

Tresset [83]

Answer:

is that even possible.

Step-by-step explanation:

4 0

3 years ago

Find f(7) for<br> the function<br> below.<br> F(x)=1/2 x 2^x

Anastasy [175]

Step-by-step explanation:

$\begin{aligned}\rm f(x)&=\rm\frac{1}{2}\times 2^x\\\rm f(7)&=2^{-1}\times 2^7\\&=2^{-1+7}\\&=2^{7-1}\\&=2^6\\&=2^6\\&=\bf 64\end{aligned}$

8 0

3 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

5 0

3 years ago