(a) What is the area and uncertainty in area of one side of a rectangular plastic brick that has a length of (21.4 ± 0.4) cm and a width of (9.8+ 0.1) cm? (Give your answers in cm².) 209.72 X 6.06 x) cm² (b) What If? If the thickness of the brick is (1.2 0.1) cm, what is the volume of the brick and the uncertainty in this volume? (Give your answers in cm³.) 12 1422
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- Physical units in mechanics are usually some combination of the dimensions time T, mass M, and length L. Consider the physical quantities m, r, u, a, and t with dimensions [m] = M, [r] = L, [u] = LT-, [a] = LT-2, and [1] = T. Enter the dimensional expression of the quantity on the right-hand side of each equation. Your answers may contain only M, L, T, and exponents. Assume that each of the following equations is dimensionally consistent. Lo = mur [Lo] = W = mar [W] = TThe sides of a small rectangular box are measured to be (1.90 ± 0.01) cm, (2.00 ± 0.02) cm, and (3.1 ± 0.1) cm long. Calculate its volume and uncertainty in cm³. a. Its volume is b. The uncertainty on its volume is cm³. cm³.(a) How many significant figures are in the numbers 999.0 and 1000.0? 999.01000.0 (b) If the uncertainty in each number is 10, what is the percent uncertainty in each? (Give your answer to 4 significant figures.) 999.0 %1000.0 % (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?
- 3.A rectangular block of wood is measured to have the dimensions 11.2 cm, 3.4 cm and 4.10 cm. Compute the volume of the block using the rules of significant figures. O 1.645 x 10² cm² a) b) 16 x 10² m² c) 1.6 x 10² cm² d) 1.60x 10² cm² Question 8 (Mandatory) (10 points) Saved 0:21A rectangle has a length of (5.1 ± 0.2) m and a width of (2.3 ± 0.1) m. Calculate: (a) the area and (b) the perimeter of the rectangle, Give the uncertainty in each value.
- How many significant figures are there in (a) 0.0210, (b) 5.060, (c) 7.10 * 10-4,(d) 1.0 * 105?A rectangle has a length of (2.8 ± 0.2) m and a width of (1.7 ± 0.2) m. Calculate the area and the perimeter of the rectangle, and give the uncertainty in each value. (a) Calculate the area and give its uncertainty. (Enter your answers in m2.) m2 ± m2 (b) Calculate the perimeter of the rectangle and give its uncertainty. (Enter your answers in m.) m ± m- Your answer is partially correct. A partly-full paint can has 0.515 U.S. gallons of paint left in it. (a) What is the volume of the paint, in cubic meters? (b) If all the remaining paint is used to coat a wall evenly (wall area = 12.1 m²), how thick is the layer of wet paint? Give your answer in meters. (a) Number i 1.949 (b) Number i 312.1 Units Units m^3 m^2
- The radius of a sphere is known to be r = 6.27 ± 0.06 cm. The volume of a sphere is given by (4/3)?r3. Find the absolute uncertainty and the percent uncertainty in the volume of the sphere. absolute uncertainty cm3 percent uncertainty(a) A pyramid has a height of 465 ft and its base covers an area of 12.0 acres (see figure below). The volume of a pyramid is given by the expression V = 1 3 -Bh, where B is the area of the base and h is the height. Find the volume of this pyramid in cubic meters. (1 acre = 43,560 ft²) 2294276.22 m³ (b) What If? If the height of the pyramid were increased to 520 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase? 99.95 X %7. A cylinder ħas á radius of 4.6 ± 0.4 cm and a height of 5.36 ± 0.3 cm. (a) Find the volume of this cylinder and its uncertainty in cubic centimeters. (Hint: The formula for the volume of a cylinder is V = TT r2 h.) (b) Find the % uncertainty for r, h and V. (c) Find the volume of this cylinder in cubic meters. 2 3 4 r with the appropriate ing water, heated by heat. Beakers 1 and 2 of water. The height of of the flame under ine the change in