By converting 900000cm³ into liters, answer will be
Answer: D
One litre is 1000 cubic centimetres.
\[ 900{,}000 \text{ cm}^{3} = \frac{900{,}000}{1000} = 900 \text{ litres} \]
Dividing by 100 or by 10,000 gives 9000 and 90, the two distractors either side. It helps to remember that a cubic metre - 1,000,000 cm³ - is exactly 1000 litres, so 900 litres is a little under a cubic metre.
Please log in or register to report this question.
A wooden cylinder to be carved is 12 cm long and has a diameter of 45 mm. Taking \( \pi = 3.142 \), its total surface area is
Answer: C
Convert the diameter to centimetres first, then halve it.
\[ 45 \text{ mm} = 4.5 \text{ cm} \quad\Longrightarrow\quad r = 2.25 \text{ cm} \]
\[ \text{TSA} = 2\pi r (r + h) = 2 \times 3.142 \times 2.25 \times (2.25 + 12) \]
\[ = 14.139 \times 14.25 = 201.5 \approx 201 \text{ cm}^{2} \]
Both flat ends count, since the whole cylinder is carved; the curved surface alone would come to about 169.7 cm².
Please log in or register to report this question.
If 200 liters of orange juice is to be poured in cylindrical drum with diameter of 80cm then depth of orange juice in drum is
Answer: B
Convert the volume to cubic centimetres and halve the diameter, then divide by the cross-sectional area.
\[ 200 \text{ litres} = 200{,}000 \text{ cm}^{3}, \qquad r = 40 \text{ cm} \]
\[ \text{cross-section} = \pi r^{2} = 3.142 \times 1600 = 5027.2 \text{ cm}^{2} \]
\[ \text{depth} = \frac{200{,}000}{5027.2} = 39.78 \text{ cm} \]
The litre-to-cubic-centimetre step is the one that decides the order of magnitude; leaving the volume in litres would give a depth of about 0.04 cm.
Please log in or register to report this question.
If a rectangular cuboid is 15 cm long, 10 cm wide and 9 cm high, then the total surface area of the cuboid is
Answer: A
A cuboid's total surface area sums its three pairs of faces.
\[ \text{TSA} = 2(lb + bh + hl) \]
\[ = 2(15 \times 10 + 10 \times 9 + 9 \times 15) \]
\[ = 2(150 + 90 + 135) = 2(375) = 750 \text{ cm}^{2} \]
Each product must be counted twice, once for each of the opposite faces - the single sum of 375 is exactly half the answer.
Please log in or register to report this question.
If a rectangular cuboid is 9cm long and 8cm wide with volume of 450cm³ then height of cuboid in 'cm' is
Answer: B
Rearrange the cuboid volume formula for the missing dimension.
\[ V = l \times b \times h \quad\Longrightarrow\quad h = \frac{V}{l \times b} \]
\[ h = \frac{450}{9 \times 8} = \frac{450}{72} = 6.25 \text{ cm} \]
Checking: \( 9 \times 8 \times 6.25 = 450 \) cm³, as required.
Please log in or register to report this question.
A closed wooden box has internal dimensions 80 cm long, 48 cm wide and 20 cm deep, and the wood is 4 cm thick. What volume of wood is used in constructing the box?
Answer: B
The wood occupies the space between the outer box and the hollow inside it, so find both volumes and subtract.
The wood is 4 cm thick on every face, so each external dimension exceeds the internal one by \( 2 \times 4 = 8 \) cm:
\[ 88 \times 56 \times 28 \text{ cm} \]
\[ V_{\text{external}} = 88 \times 56 \times 28 = 137{,}984 \text{ cm}^{3} \]
\[ V_{\text{internal}} = 80 \times 48 \times 20 = 76{,}800 \text{ cm}^{3} \]
\[ V_{\text{wood}} = 137{,}984 - 76{,}800 = 61{,}184 \text{ cm}^{3} \]
Adding 4 cm rather than 8 cm to each dimension is the standard error - the thickness is present on both opposite faces.
Please log in or register to report this question.
Water flows through a pipe of diameter 86 mm at a rate of 5 m/s. The volume of water discharged per minute is
Answer: D
The water leaving in one minute forms a cylinder whose cross-section is the pipe's and whose length is the distance the flow covers in that minute.
\[ d = 86 \text{ mm} = 0.086 \text{ m} \quad\Longrightarrow\quad r = 0.043 \text{ m} \]
\[ \text{length per minute} = 5 \times 60 = 300 \text{ m} \]
\[ V = \pi r^{2} \times 300 = 3.1416 \times (0.043)^{2} \times 300 \]
\[ = 3.1416 \times 0.001849 \times 300 = 1.7429 \text{ m}^{3} \]
Since \( 1 \text{ m}^{3} = 1000 \) litres:
\[ V \approx 1742.87 \text{ litres} \]
The two conversions - millimetres to metres and seconds to minutes - are what set the scale of the answer.
Please log in or register to report this question.
Non-right pyramids are called
Answer: A
A pyramid is called a right pyramid when its apex sits directly above the centre of its base, so the axis meets the base at a right angle.
When the apex is displaced sideways, the axis leans and the pyramid is oblique.
The other options name pyramids by the shape of their base - triangular, pentagonal, hexagonal - which is a separate classification altogether. A hexagon-based pyramid can be either right or oblique.
Please log in or register to report this question.
The volume of a cone whose base diameter is 7 cm and whose height is 14 cm is
Answer: C
Halve the diameter to get the base radius, then use the cone volume formula with \( \pi = \tfrac{22}{7} \).
\[ r = \frac{7}{2} = 3.5 \text{ cm}, \qquad h = 14 \text{ cm} \]
\[ V = \frac{1}{3}\pi r^{2} h = \frac{1}{3} \times \frac{22}{7} \times (3.5)^{2} \times 14 \]
\[ = \frac{1}{3} \times \frac{22}{7} \times 12.25 \times 14 = \frac{1}{3} \times 539 \]
\[ V \approx 180 \text{ cm}^{3} \]
Forgetting the \( \tfrac{1}{3} \) would give the volume of the enclosing cylinder, three times too large.
Please log in or register to report this question.
A cone has a circular base of radius 6m and volume 84π m³. height of cone is
Answer: A
Rearrange the cone volume formula for the height. The \( \pi \) appears on both sides and cancels.
\[ V = \frac{1}{3}\pi r^{2} h \quad\Longrightarrow\quad 84\pi = \frac{1}{3}\pi (6)^{2} h \]
\[ 84 = \frac{36h}{3} = 12h \]
\[ h = 7 \text{ m} \]
Because the volume is quoted as a multiple of \( \pi \), no decimal approximation is needed anywhere.
Please log in or register to report this question.
